{"Affiliation":[{"label":"Affiliation","value":"Applied Science, Faculty of","attrs":{"lang":"en","ns":"http:\/\/vivoweb.org\/ontology\/core#departmentOrSchool","classmap":"vivo:EducationalProcess","property":"vivo:departmentOrSchool"},"iri":"http:\/\/vivoweb.org\/ontology\/core#departmentOrSchool","explain":"VIVO-ISF Ontology V1.6 Property; The department or school name within institution; Not intended to be an institution name."},{"label":"Affiliation","value":"Civil Engineering, Department of","attrs":{"lang":"en","ns":"http:\/\/vivoweb.org\/ontology\/core#departmentOrSchool","classmap":"vivo:EducationalProcess","property":"vivo:departmentOrSchool"},"iri":"http:\/\/vivoweb.org\/ontology\/core#departmentOrSchool","explain":"VIVO-ISF Ontology V1.6 Property; The department or school name within institution; Not intended to be an institution name."}],"AggregatedSourceRepository":[{"label":"AggregatedSourceRepository","value":"DSpace","attrs":{"lang":"en","ns":"http:\/\/www.europeana.eu\/schemas\/edm\/dataProvider","classmap":"ore:Aggregation","property":"edm:dataProvider"},"iri":"http:\/\/www.europeana.eu\/schemas\/edm\/dataProvider","explain":"A Europeana Data Model Property; The name or identifier of the organization who contributes data indirectly to an aggregation service (e.g. Europeana)"}],"Campus":[{"label":"Campus","value":"UBCV","attrs":{"lang":"en","ns":"https:\/\/open.library.ubc.ca\/terms#degreeCampus","classmap":"oc:ThesisDescription","property":"oc:degreeCampus"},"iri":"https:\/\/open.library.ubc.ca\/terms#degreeCampus","explain":"UBC Open Collections Metadata Components; Local Field; Identifies the name of the campus from which the graduate completed their degree."}],"Creator":[{"label":"Creator","value":"McDowall, Bruce J.","attrs":{"lang":"en","ns":"http:\/\/purl.org\/dc\/terms\/creator","classmap":"dpla:SourceResource","property":"dcterms:creator"},"iri":"http:\/\/purl.org\/dc\/terms\/creator","explain":"A Dublin Core Terms Property; An entity primarily responsible for making the resource.; Examples of a Contributor include a person, an organization, or a service."}],"DateAvailable":[{"label":"DateAvailable","value":"2010-04-13T15:20:12Z","attrs":{"lang":"en","ns":"http:\/\/purl.org\/dc\/terms\/issued","classmap":"edm:WebResource","property":"dcterms:issued"},"iri":"http:\/\/purl.org\/dc\/terms\/issued","explain":"A Dublin Core Terms Property; Date of formal issuance (e.g., publication) of the resource."}],"DateIssued":[{"label":"DateIssued","value":"1982","attrs":{"lang":"en","ns":"http:\/\/purl.org\/dc\/terms\/issued","classmap":"oc:SourceResource","property":"dcterms:issued"},"iri":"http:\/\/purl.org\/dc\/terms\/issued","explain":"A Dublin Core Terms Property; Date of formal issuance (e.g., publication) of the resource."}],"Degree":[{"label":"Degree","value":"Master of Applied Science - MASc","attrs":{"lang":"en","ns":"http:\/\/vivoweb.org\/ontology\/core#relatedDegree","classmap":"vivo:ThesisDegree","property":"vivo:relatedDegree"},"iri":"http:\/\/vivoweb.org\/ontology\/core#relatedDegree","explain":"VIVO-ISF Ontology V1.6 Property; The thesis degree; Extended Property specified by UBC, as per https:\/\/wiki.duraspace.org\/display\/VIVO\/Ontology+Editor%27s+Guide"}],"DegreeGrantor":[{"label":"DegreeGrantor","value":"University of British Columbia","attrs":{"lang":"en","ns":"https:\/\/open.library.ubc.ca\/terms#degreeGrantor","classmap":"oc:ThesisDescription","property":"oc:degreeGrantor"},"iri":"https:\/\/open.library.ubc.ca\/terms#degreeGrantor","explain":"UBC Open Collections Metadata Components; Local Field; Indicates the institution where thesis was granted."}],"Description":[{"label":"Description","value":"The duration of load problem in wood subjected to stresses in tension perpendicular to the grain is studied both analytically and experimentally. Analytically, viscoelastic models derived from the principles of fracture mechanics are developed and discussed with respect to their application to the failure mechanism of wood in tension and bending. To assess the accuracy of the predictions of these models, they are compared against the experimental results from duration of load tests carried out on Douglas fir in tension perpendicular to the grain. This failure mode is hypothesised as representative of the critical failure initiating mode of commercial material. A specimen design was developed which proved very successful in keeping the coefficient of variation of the short term strength quite low for wood, approximately 10%. This low variability enabled the tests to be carried out with sample sizes much smaller than those used in the duration of load testing of commercial material.","attrs":{"lang":"en","ns":"http:\/\/purl.org\/dc\/terms\/description","classmap":"dpla:SourceResource","property":"dcterms:description"},"iri":"http:\/\/purl.org\/dc\/terms\/description","explain":"A Dublin Core Terms Property; An account of the resource.; Description may include but is not limited to: an abstract, a table of contents, a graphical representation, or a free-text account of the resource."}],"DigitalResourceOriginalRecord":[{"label":"DigitalResourceOriginalRecord","value":"https:\/\/circle.library.ubc.ca\/rest\/handle\/2429\/23404?expand=metadata","attrs":{"lang":"en","ns":"http:\/\/www.europeana.eu\/schemas\/edm\/aggregatedCHO","classmap":"ore:Aggregation","property":"edm:aggregatedCHO"},"iri":"http:\/\/www.europeana.eu\/schemas\/edm\/aggregatedCHO","explain":"A Europeana Data Model Property; The identifier of the source object, e.g. the Mona Lisa itself. This could be a full linked open date URI or an internal identifier"}],"FullText":[{"label":"FullText","value":"CJ THE DURATION OF LOAD EFFECT IN TENSION PERPENDICULAR TO THE GRAIN FOR DOUGLAS FIR. BY Bruce J . McDowall B.E.(Hons)., The U n i v e r s i t y of Auckland, New Zealand, 1979 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE MASTER OF APPLIED SCIENCE i n THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF CIVIL ENGINEERING We accept t h i s t h e s i s as conforming to the r e q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA September, 1982. \u00a9 Bruce J . McDowall, 1982. In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree at the U n i v e r s i t y o f B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and study. I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the head of my department or by h i s o r her r e p r e s e n t a t i v e s . I t i s understood t h a t copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be allowed without my w r i t t e n p e r m i s s i o n . Department of (CiUll- ^ \/ 0 6 \/ A J 5 V \" R W 6 The U n i v e r s i t y of B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 DE-6 (3\/81) i i ABSTRACT The d u r a t i o n of l o a d problem i n wood s u b j e c t e d to s t r e s s e s in t e n s i o n p e r p e n d i c u l a r to the g r a i n i s s t u d i e d both a n a l y t i c a l l y and e x p e r i m e n t a l l y . A n a l y t i c a l l y , v i s c o e l a s t i c models d e r i v e d from the p r i n c i p l e s of f r a c t u r e mechanics are developed and d i s c u s s e d with r e s p e c t to t h e i r a p p l i c a t i o n to the f a i l u r e mechanism of wood i n t e n s i o n and bending. To assess the accuracy of the p r e d i c t i o n s of these models, they are compared a g a i n s t the experimental r e s u l t s from d u r a t i o n of loa d t e s t s c a r r i e d out on Douglas f i r i n t e n s i o n p e r p e n d i c u l a r to the g r a i n . T h i s f a i l u r e mode i s hypothesised as r e p r e s e n t a t i v e of the c r i t i c a l f a i l u r e i n i t i a t i n g mode of commercial m a t e r i a l . A specimen design was developed which proved very s u c c e s s f u l i n keeping the c o e f f i c i e n t of v a r i a t i o n of the short term s t r e n g t h q u i t e low f o r wood, approximately 10%. T h i s low v a r i a b i l i t y enabled the t e s t s to be c a r r i e d out with sample s i z e s much smal l e r than those used i n the d u r a t i o n of loa d t e s t i n g of commercial m a t e r i a l . i i i ACKNOWLEDGEMENTS The author would l i k e t o express h i s g r a t i t u d e to h i s re s e a r c h a d v i s o r P r o f e s s o r Borg Madsen, Dept of C i v i l E n g i n e e r i n g f o r h i s guidance support and i n s p i r a t i o n throughout t h i s r e s e a r c h p r o j e c t . He would a l s o l i k e to thank the Department of C i v i l E n g i n e e r i n g t e c h n i c i a n s f o r t h e i r w i l l i n g a s s i s t a n c e i n the manufacture of the apparatus, and h e l p f u l s u g g e s t i o n s . A l s o the f o l l o w i n g people: John S o l e s , B i l l L i p s e t t , Andy Buchanan, Mike McNab, Wally Kee, Alex A p o s t o l i , A l G r o f f , Dana Soong and Diane S o l e s are thanked f o r t h e i r a s s i s t a n c e i n s e t t i n g up and moni t o r i n g two of the experiments. A l s o Dr Ken Johns, Dean of E n g i n e e r i n g at the U n i v e r s i t y of Sherbrooke, who while on s a b b a t i c a l leave at UBC, gave h e l p f u l comments and c r i t i c i s m s at d i f f e r e n t stages of the work. Dr R.O. F o s c h i , adjunct p r o f e s s o r at the U n i v e r s i t y of B r i t i s h Columbia, i s thanked f o r h i s c r i t i c i s m s on the work and fo r h i s suggestions of improvements. In a d d i t i o n Dr D.L. Anderson, p r o f e s s o r at the U n i v e r s i t y of B r i t i s h Columbia, f o r h i s h e l p i n the i n t e r p r e t a t i o n of the v i s c o e l a s t i c models. F i n a l l y the r e s e a r c h a s s i s t a n t s h i p funded by an NSERC grant and a grant of lumber from Bay F o r e s t Products L t d , Vancouver, B.C., are g r a t e f u l l y acknoweldged. i v TABLE OF CONTENTS. CHAPTER 1 INTRODUCTION 1 1.1 D e f i n i t i o n Of The D u r a t i o n Of Load E f f e c t 1 1.2 Background 1 1 .3 Scope 4 1.3.1 I n t r o d u c t i o n 4 1.3.2 The N i e l s e n Model 4 1.3.3 The Step-wise Model 4 1.3.4 S t r e n g t h E f f e c t 4 1.3.5 Mo i s t u r e Content 5 1.3.6 C y c l i c Loading 5 1.4 Summary Of O b j e c t i v e s 6 CHAPTER 2 THEORY 7 2.1 I n t r o d u c t i o n 7 2.2 Models For Duration Of Load 7 2.3 General Theory Of V i s c o e l a s t i c F r a c t u r e Mechanics ... 10 2.4 The Step-Wise Model For The Duration Of Load E f f e c t . 14 2.5 The N i e l s e n Model For The D u r a t i o n Of Load E f f e c t . . 19 2.6 Comparison Of The N i e l s e n And Step-wise Models 22 2.7 Evidence For The N i e l s e n And Step-wise Models 25 2.7.1 I n t r o d u c t i o n 25 2.7.2 Experimental Evidence 26 2.7.3 Q u a l i t a t i v e Evidence 28 2.8 Summary 29 CHAPTER 3 EXPERIMENT DESIGN 30 3.1 I n t r o d u c t i o n L 30 3.2 Crack O r i e n t a t i o n And Propagation 31 3.3 Specimen Development 34 3.4 Apparatus i* \u2022 \u2022 r 3 6 3.5 Specimen P r e p a r a t i o n I 37 3.6 Tes t Procedure X . 38 3.7 Data A n a l y s i s .Vr- 39 3.8 Determination Of Ts 42 3.9 E r r o r s 44 3.10 Summary 45 CHAPTER 4 RESULTS 46 4.1 I n t r o d u c t i o n 46 4.2 Experiment D e s c r i p t i o n s 47 4.2.1 Experiment No. 1 , C y c l i c - 1 47 4.2.2 Experiment No.2, Two Crack Lengths 48 4.2.3 Experiment No.3, Three Crack Lengths 50 4.2.4 Experiment No.4, C y c l i c - 2 51 4.2.5 Experiment No.5, Mo i s t u r e Test 52 4.2.6 Experiment No.6, Ts 53 4.3 Summary 55 CHAPTER 5 DISCUSSION 56 5.1 I n t r o d u c t i o n 56 5.2 Experimental Method And A n a l y s i s 56 5.2.1 The Normal D i s t r i b u t i o n 56 V 5.2.2 F r a c t u r e Toughness 57 5.2.3 F i t Of The Creep And L i m i t S t r e n g t h Parameters .. 59 5.2.4 Short Term Str e n g t h B i a s 60 5.2.5 F i n i t e - I n f i n i t e Medium Adjustment 61 5.3 Creep F u n c t i o n s And Parameters 63 5.3.1 I n t r o d u c t i o n 63 5.3.2 Creep F u n c t i o n s 64 5.3.3 Creep Parameters 64 5.4 The Ts Experiment 66 5.5 Moisture Content E f f e c t 68 5.6 Str e n g t h E f f e c t 70 5.7 D e n s i t y E f f e c t 72 5.8 C y c l i c Loading 73 5.9 Confidence L i m i t s 75 5.10 General L i m i t a t i o n s 76 5.10.1 Ts Experiment 76 5.10.2 S t r e n g t h E f f e c t ; 77 CHAPTER 6 CONCLUSIONS 79 6.1 I n t r o d u c t i o n 79 6.2 Summary 80 6.3 F u r t h e r Research And A p p l i c a t i o n s 81 REFERENCES 84 FIGURES 8 7 APPENDICES 1 2 7 Appendix 1 Test Data 127 Appendix 2 Volume E f f e c t 140 Appendix 3 F a i l u r e C r i t e r i o n 141 Appendix 4 Adjustment C a l c u l a t i o n s 142 Appendix 5 A Step-wise Value For P l a s t i c Y i e l d S t r e s s .148 ABSTRACT \u2022 i i ACKNOWLEDGMENTS i 1 1 TABLE OF CONTENTS i v LIST OF FIGURES v i v i LIST OF FIGURES 1 S t r e s s F i e l d At The Crack T i p 88 2 T y p i c a l D uration Of Load P l o t For The Step-wise Model .. 89 3 N i e l s e n And Step-wise Model P l o t s 90 4 R e s u l t s Of Schniewind And Centeno( 1973) 91 5 R e s u l t s Of Bach(l975) 92 6 R e s u l t s Of Debaise Et A l . 0 9 6 6 ) 93 7 The Three Modes Of F a i l u r e 94 8 Induced S t r e s s e s In Tension Perp. To The G r a i n 95 9 Unprepared Specimen 96 10 Mounted Specimen 97 11 Specimen With I n s t r o n Tensometer Attached 98 12 Diagrammatical Specimen, And Crack I n i t i a t i o n 99 13 Apparatus (Diagrammatical) 100 14 Apparatus - 101 15 Apparatus 102 16 Ts Determination 103 17 Ts Determination 103 18 D u r a t i o n Of Load P l o t For Experiment 1 104 19 D u r a t i o n Of Load P l o t For Experiment 2 105 20 Duration Of Load P l o t For Experiment 3 106 21 D u r a t i o n Of Load P l o t For Experiment 4 107 22 D u r a t i o n Of Load P l o t For Experiment 5 108 23 D u r a t i o n Of Load P l o t For Experiment 6 109 24 Ts (Expt 6) S u r v i v o r Strengths 110 25 Normal F i t To Short Term Strength Data, Expt 6 111 26 Tada P a r i s I r w i n d 9 7 3 ) 112 27 E f f e c t Of \"a\" And \"b\" Upon The Duration Of Load P l o t ..113 28 E f f e c t Of \u00ab, \u00ab y 0 and Upon The Duration Of Load P l o t .114 29 Creep Parameters, K a s s d 9 6 9 ) 115 30 Creep Parameters, K a s s d 9 6 9 ) 116 31 Creep Parameters, Schniewind And Barrett(1972) 117 32 Creep Parameters, Schniewind And B a r r e t t ( 1972) 1 17 33 Step-Wise F i t To Expt 6 (Ts) 118 34 N i e l s e n F i t To Expt 6 (Ts) 119 35 Step-Wise F i t To Moisture T e s t , Expt 5 120 36 Step-wise F i t To Expt 2 121 37 Step-wise F i t To Expt 3 122 38 N i e l s e n F i t To Expt 3 123 39 Step-wise F i t To Expt 1 124 40 Step-wise F i t To Expt 4 125 41 Confidence L i m i t s On The S t r e s s R a t i o 126 A1 Volume E f f e c t P l o t By Barrett(1974) 140 A2 Step-wise Model Of The Crack T i p 150 1 CHAPTER 1 INTRODUCTION 1.1 D e f i n i t i o n of the Duration of Load E f f e c t The d u r a t i o n of l o a d e f f e c t i n wood can be d e f i n e d as a r e d u c t i o n of s t r e n g t h under the a c t i o n of a p e r s i s t e n t load over a p e r i o d of time. For example, a specimen of wood loaded to a s t r e s s r a t i o of 0.75 ( i . e . , 75% of i t s short term f a i l u r e s t r e s s ) w i l l not f a i l upon a p p l i c a t i o n of the l o a d . However, at some time l a t e r i t may suddenly f a i l due to a weakening of the specimen that has taken p l a c e w i t h i n that time p e r i o d . 1.2 Background. The development of the LSD code in Canada r e q u i r e s that a f r e s h look be taken at the design procedure fo r timber. Many qu e s t i o n s need to be addressed, amongst them the d u r a t i o n of l o a d phenomenon. For many years the s t r e n g t h r e d u c t i o n versus time curve developed by Wood(l95l) has been used i n design c a l c u l a t i o n s i n North America and other p a r t s of the world. The a p p l i c a b i l i t y of t h i s curve to design seems q u e s t i o n a b l e when c o n s i d e r i n g that small dry, s t r a i g h t g r a i n e d , c l e a r specimens of Douglas f i r are being used to represent commercial m a t e r i a l s , 2 o f t e n with major d e f e c t s and s t r e s s r a i s e r s such as knots, c r a c k s , g r a i n d e v i a t i o n s , e t c . The f a i l u r e of the small c l e a r t e s t s conducted i s normally i n i t i a t e d i n compression p a r a l l e l to the g r a i n . T h i s f a i l u r e mode does not represent the most f r e q u e n t l y encountered f a i l u r e mode i n commercial m a t e r i a l , where crack propagation i s observed to occur i n a plane p a r a l l e l with the g r a i n , caused e i t h e r by s t r e s s e s i n t e n s i o n p e r p e n d i c u l a r to the g r a i n induced^ at the knots, or shear s t r e s s e s . To s a t i s f y the need f o r a more a c c u r a t e treatment of the d u r a t i o n of loa d e f f e c t , c u r r e n t r e s e a r c h i s d e v e l o p i n g i n two ways. B a r r e t t and Foschi(1978a,1978b) have p o s t u l a t e d a damage accumulation model based on creep r u p t u r e . The damage rate i s given as the sum of a s t r e s s dependent term and a damage dependent term. The model al l o w s f o r a s t r e s s t h r e s h o l d below which the damage r a t e vanishes.. By c a l i b r a t i o n a g a i n s t experimental data the co n s t a n t s of the r e s u l t i n g e x p r e s s i o n can be o p t i m i s e d , to gi v e a very f l e x i b l e t o o l u s e f u l i n r e l i a b i l i t y s t u d i e s using v a r i o u s l o a d i n g h i s t o r i e s . Gerhards(1979) a l s o proposes a s i m i l a r model. The theory of v i s c o e l a s t i c f r a c t u r e mechanics has been a p p l i e d to the d u r a t i o n of load e f f e c t i n wood. The ba s i c assumption i s that crack propagation i n wood i s of a l i n e a r v i s c o e l a s t i c - p l a s t i c nature. In order to p r e d i c t the time to f a i l u r e , the necessary m a t e r i a l behaviour and parameters are chosen and the e x p r e s s i o n s d e r i v e d . Nielsen(1978,1980) and Kousholt(1980) using one set of parameters have d e r i v e d a model 3 (now r e f e r r e d to as the N i e l s e n model) where the crack i s s a i d to lengthen i n a continuous f a s h i o n . Brincker(1981,1982) d e r i v e s a model with c h a r a c t e r i s t i c s very s i m i l a r to those of the N i e l s e n model. However, one m a t e r i a l parameter i s d i f f e r e n t , and the cra c k i s assumed t o lengthen i n small s p u r t s . T h i s model w i l l be r e f e r r e d to as the step-wise model. Johns and Madsen (1982) have a p p l i e d the theory of the N i e l s e n model to commercial 2\"x6\" Douglas f i r boards i n bending ( f a i l u r e i n i t i a t e d i n t e n s i o n p e r p e n d i c u l a r to the g r a i n ) under constant s t r e s s , and have found good agreement between experiment and theory. I t i s the N i e l s e n and the step-wise models that t h i s r e s e a r c h i s aimed at i n v e s t i g a t i n g . These models have a f i r m foundation upon the concepts of f r a c t u r e mechanics, and u n l i k e e m p i r i c a l models u t i l i z e m a t e r i a l parameters which are seen to have a p h y s i c a l s i g n i f i c a n c e . These f e a t u r e s g i v e the v i s c o e l a s t i c models p o t e n t i a l to represent the d u r a t i o n of load behaviour i n wood. In order to t e s t the v i s c o e l a s t i c models i n the most r e a l i s t i c manner, i t was decided that c r a c k s propagating l o n g i t u d i n a l l y , s t r e s s e d i n t e n s i o n p e r p e n d i c u l a r to the g r a i n i n the opening mode be used. For reasons e x p l a i n e d i n Chapter 3 t h i s mode of f a i l u r e was expected to be r e p r e s e n t a t i v e of the c r i t i c a l f a i l u r e i n i t i a t i o n mode i n commercial m a t e r i a l and i t i s p o s t u l a t e d that t h i s r e p r e s e n t s a lower bound or worst case f o r d u r a t i o n of l o a d behaviour of commercial m a t e r i a l . 4 1.3 Scope. 1.3.1 I n t r o d u c t i o n . In order to i n v e s t i g a t e the v i s c o e l a s t i c models, experiments were c a r r i e d out and t h e i r r e s u l t s compared with the p r e d i c t i o n s of the v i s c o e l a s t i c models. In p a r t i c u l a r , the experiments were designed to i n v e s t i g a t e the f o l l o w i n g f e a t u r e s . 1.3.2 The N i e l s e n model. To determine e x p e r i m e n t a l l y the a p p l i c a b i l i t y of the N i e l s e n model to wood, by v a r y i n g c r i t i c a l parameters and comparing the p r e d i c t e d behaviour to the experimental r e s u l t . 1.3.3 The Step-wise model. To determine e x p e r i m e n t a l l y the a p p l i c a b i l i t y of the s t e p -wise model to wood, by v a r y i n g c r i t i c a l parameters and comparing the p r e d i c t e d behaviour to the experimental r e s u l t . 1.3.4 Strength E f f e c t . One of the f e a t u r e s of the N i e l s e n and step-wise models i s that they both p r e d i c t a s t r e n g t h e f f e c t . For example, f o r two separate groups of specimens, each group with a d i f f e r e n t average short term s t r e n g t h , loaded to the same s t r e s s r a t i o , 5 the times to f a i l u r e w i l l be d i f f e r e n t . The higher s t r e n g t h specimens should f a i l e a r l i e s t . To t e s t t h i s aspect of the t h e o r i e s , h i g h s t r e n g t h specimens and low s t r e n g t h specimens are t e s t e d at the same s t r e s s r a t i o and t h e i r r e l a t i v e behaviours compared. 1.3.5 Moisture Content. In the past r e s e a r c h has been c a r r i e d out to t e s t the e f f e c t of moisture content on creep ( i n c r e a s e d moisture content tends to g i v e i n c r e a s e d c r e e p ) . However the r e l a t i o n s h i p between moisture content and the d u r a t i o n of lo a d e f f e c t has not been e s t a b l i s h e d . T h i s p a r t of the study attempts to l i n k the i n c r e a s e d creep due to a higher moisture content, to e a r l i e r f a i l u r e times i n the d u r a t i o n of l o a d e f f e c t as p r e d i c t e d by the N i e l s e n and step-wise models. Ther e f o r e specimens of high moisture content are t e s t e d , and t h e i r behaviour compared with the behaviour of somewhat drye r specimens. 1.3.6 C y c l i c Loading. T r a d i t i o n a l l y when d e s i g n i n g a wooden s t r u c t u r e , i t i s necessary to determine the maximum design load, (which f o r r o o f s i n Canada i s o f t e n the snow l o a d ) . T h i s maximum snow loa d i s assumed to a c t f o r a t o t a l of only two months d u r i n g the l i f e of the b u i l d i n g . T h e r e f o r e a d u r a t i o n of lo a d f a c t o r of 1.15 i s used a c c o r d i n g to the Madison Curve developed by Wood(l95l). 6 More r e a l i s t i c a l l y , a s e r i e s of annual snow loads i s a p p l i e d , not a l l of the them the maximum design l o a d . In order that the d u r a t i o n of l o a d behaviour of t h i s l o a d i n g c h a r a c t e r i s t i c be b e t t e r understood, i t was deci d e d that a simple experiment be performed. By means of comparative t e s t s between samples loaded c o n t i n u o u s l y and samples loaded f o r s e v e r a l p e r i o d s of time adding up to the c o n t i n u o u s l y loaded time, the obj e c t was to determine i f a d i f f e r e n c e i n the d u r a t i o n of loa d e f f e c t e x i s t s f o r these d i f f e r e n t l o a d i n g h i s t o r i e s . 1.4 Summary of O b j e c t i v e s . 1. To i n v e s t i g a t e the d u r a t i o n of loa d behaviour i n t e n s i o n p e r p e n d i c u l a r to the g r a i n over time p e r i o d s between one hour and three months, and compare with t h a t p r e d i c t e d by the models based on the theory of v i s c o e l a s t i c f r a c t u r e mechanics as proposed by N i e l s e n and by B r i n c k e r . 2. To i n v e s t i g a t e the e f f e c t of the a p p l i e d s t r e s s l e v e l upon the d u r a t i o n of load e f f e c t . 3. To i n v e s t i g a t e the e f f e c t of a high moisture content upon the d u r a t i o n of load e f f e c t . 4. To i n v e s t i g a t e the e f f e c t of recovery p e r i o d s ( c y c l i c l o a d i n g ) upon the d u r a t i o n of l o a d e f f e c t . 5. To comment upon the o b s e r v a t i o n s reached, t h e i r subsequent a p p l i c a t i o n s to design p r a c t i c e and suggested d i r e c t i o n s f o r f u r t h e r r e s e a r c h . 7 CHAPTER 2 THEORY 2 . 1 I n t r o d u c t i o n . This chapter e x p l a i n s the basic assumptions and theory of the N i e l s e n and step-wise models, along with other models for du r a t i o n of loa d . I t then o u t l i n e s the theory of the Nie l s e n and step-wise models and demonstrates the ready a p p l i c a t i o n of both models to the larg e body of research already a v a i l a b l e i n the f i e l d s of f r a c t u r e mechanics and dur a t i o n of load i n wood. 2 . 2 Models For Duration Of Load. Models for du r a t i o n of load take one of f i v e forms: r e g r e s s i o n to s t r a i g h t l i n e s or curves, regression to a proposed mathematical model, phenomenological approaches, l i n e a r f r a c t u r e mechanics models, or v i s c o e l a s t i c f r a c t u r e mechanics models. T r a d i t i o n a l l y , regressions to a s t r a i g h t l i n e on semi-log paper have been most widely used. In f a c t , f o r an experiment c a r r i e d out w i t h i n a l i m i t e d time domain, these regressions give a good f i t to the trend of the data. They f a i l abysmally however, when the r e s u l t s of one researcher are compared with those of another; no r a t i o n a l e can be provided to l i n k the two 8 because of the inescapable v a r i a t i o n s i n m a t e r i a l p r o p e r t i e s and t e s t c o n d i t i o n s . These r e g r e s s i o n s do however p r o v i d e a good r e c o r d of d u r a t i o n of l o a d experiments performed i n the past, and as such are a very v a l u a b l e source of i n f o r m a t i o n f o r the understanding of the d u r a t i o n of l o a d behaviour of f u l l s c a l e members. Rec e n t l y , more f l e x i b l e mathematical models, as proposed by Gerhards(1979) and B a r r e t t and Foschi(1978a,1978b) are being used. These models i n c o r p o r a t e the concept of accumulating damage and t h e r e f o r e p r o g r e s s i v e f a i l u r e ( b e a r i n g a c l o s e resemblance t o the f a t i g u e equations of m e t a l s ) , thus y i e l d i n g a f l e x i b l e model f o r d u r a t i o n of l o a d . A good f i t to the experimental data can be ob t a i n e d . The damage accumulation model i s h i g h l y developed, t o the p o i n t where the inherent v a r i a b i l i t y of each parameter i s c o n s i d e r e d , so that the model i s very u s e f u l i n c a r r y i n g out r e l i a b i l i t y s t u d i e s f o r v a r y i n g l o a d h i s t i o r i e s and l o a d i n g c o n d i t i o n s . Other f a i l u r e p r e d i c t i n g c r i t e r i a are based upon energy methods. For example, the C r i t i c a l T o t a l Energy method p r e d i c t s f a i l u r e to occur when the t o t a l energy transformed i n the m a t e r i a l reaches a c e r t a i n v a l u e . The C r i t i c a l R e v e r s i b l e Energy method (o f t e n r e f e r r e d to as the Reiner Weisenberg f a i l u r e c r i t e r i o n ) uses K e l v i n c h a i n s and dashpots t o model m a t e r i a l behaviour, and f a i l u r e i s p r e d i c t e d to occur when the e l a s t i c a l l y s t o r e d energy reaches . a c r i t i c a l v a l u e . These methods are c a l l e d phenomenological. They o f f e r a p h y s i c a l i n t e r p r e t a t i o n of behaviour but are not based on p h y s i c a l 9 f a i l u r e mechanisms. Thus i f l i n e a r c o n s t i t u t i v e equations are a p p l i e d , they can not account f o r accumulating damage as does the crack propagation mechanism of f r a c t u r e mechanics. Mindess Nadeau and Barrett(1975,1976), and Mindess B a r r e t t and Spencer(1979) c a r r i e d out t e s t s on Douglas f i r i n t e n s i o n p e r p e n d i c u l a r to the g r a i n u s i n g bending and double t o r s i o n methods. By assuming the p r i n c i p l e s of l i n e a r f r a c t u r e mechanics, the r e s e a r c h e r s developed an experimental and a n a l y t i c a l method whereby long term d u r a t i o n of l o a d behaviour was e x t r a p o l a t e d from the r e s u l t s of r e l a t i v e l y short d u r a t i o n t e s t s . They concluded, however, that the i n v e s t i g a t i o n s were \"...not very f r u i t f u l . . . \" , and that a more g e n e r a l model a b l e to i n c l u d e v i s c o e l a s t i c and time dependent e f f e c t s was r e q u i r e d . Although f r a c t u r e mechanics i n wood has been s t u d i e d f o r many yea r s , r e s e a r c h has always tended to be segmental i n nature, l a c k i n g a model capable of l i n k i n g together the many f a c e t s of f r a c t u r e i n wood. Creep experiments, d u r a t i o n of load experiments, f r a c t u r e toughness experiments, f l u c t u a t i n g moisture content experiments and many others have been undertaken i n the r e s e a r c h l a b o r a t o r i e s of the world on v a r y i n g s p e c i e s . However, none of these have been combined in order to p r o v i d e a deeper understanding of the d u r a t i o n of load e f f e c t . T h i s e m p i r i c a l evidence r e q u i r e s a t h e o r e t i c a l framework, w i t h i n which the v a r y i n g behaviours observed can be u n i f i e d and used f o r the p r e d i c t i o n of response to c o n d i t i o n s other than those t e s t e d . The N i e l s e n and step-wise models allow t h i s , by l i n k i n g the m a t e r i a l p r o p e r t i e s w i t h i n a g e n e r a l theory where t h e i r 10 r e l a t i v e e f f e c t s upon the behaviour of wood under a s u s t a i n e d l o a d can be e v a l u a t e d , p r o v i d i n g two u s e f u l models f o r d e v e l o p i n g an understanding of the d u r a t i o n of l o a d phenomenon. 2.3 General Theory of V i s c o e l a s t i c F r a c t u r e Mechanics The important f e a t u r e s of the theory of v i s c o e l a s t i c f r a c t u r e mechanics as they apply to t h i s study, are o u t l i n e d below. Wood i s a composite m a t e r i a l c o n s i s t i n g mainly of polymers. I t i s assumed to be a homogeneous continuum and thus concepts such as s t r e s s and s t r a i n can be a p p l i e d . The concept of the very important s t r e s s i n t e n s i t y f a c t o r k i s i n t r o d u c e d and d e f i n e d Cc i s the h a l f crack l e n g t h ) . (2-1 ) k 2 = ( 1 + a ( A t \/ t , ) b ) = GE S i m i l a r l y f o r the short term s t r e n g t h c0 ( At = 0 ) (2-9) ff02nc0p = GE N o t i c e that (2-9) i s equal to the G r i f f i t h Energy Balance as i n (2-20) D e f i n i n g the s t r e s s r a t i o 9 (2-10) 9 = tfAo 18 and n o r m a l i s i n g we get (2-11) At = t,M ( ( C 0 \/ C ) ( 1 \/ 9 2 ) -1 ) , M = (1\/a) <\/b N o t i c e that t h i s equation i s only v a l i d f o r v a l u e s of c up to the c r i t i c a l c r a c k l e n g t h . When c tends t o the c r i t i c a l c rack l e n g t h , At tends to zero and the crack v e l o c i t y tends to i n f i n i t y . The equation does not d e s c r i b e the growth of the cra c k a f t e r the stage where the c r i t i c a l c rack l e n g t h has been a t t a i n e d i . e . , i t only d e s c r i b e s phase 1 and phase 2 behaviour. Phase 3 growth (very r a p i d and c a t a s t r o p h i c ) d e s c r i b e s crack growth a f t e r the c r i t i c a l crack l e n g t h has been achieved. Ts - Teat can be determined by the f o l l o w i n g where the s u b s c r i p t c r i s an a b b r e v i a t i o n f o r c r i t i c a l . T h i s i n t e g r a l can be s o l v e d n u m e r i c a l l y f o r any value of b, however i f b= 1\/2, 1\/3, or 1\/4 e t c . , then the i n t e g r a l can be expressed i n c l o s e d form such that (2-12) (2-13) Ts-Tcat = t,M ( F ( 0 ) \/ ( 9 2 * 2 ) ) 19 where (2-14) 2 = i r \/ ( 2 c 0 ) ( r e f e r a l s o to s e c t i o n 2.6) and as an example, f o r b=l\/3, (2-15) F(9) = l \/ ( 4 9 a ) - 3\/(29 2) + 9 2\/2 + 3\/4 - 3\/2 l n ( 9 2 ) From (2-11) i f c \/ c 0 = 1, then At = Ts which i m p l i e s Vb (2-16) Ts = t,M ( 1\/9 2 - 1 ) S u b s t i t u t i n g t h i s r e s u l t i n t o (2-13) then (2-17) Teat \u00bb t,M ( (1\/9 2 - D 3 + F ( 9 ) \/ ( 9 2 * 2 ) ) 2.5 The N i e l s e n Model f o r the Du r a t i o n Of Load E f f e c t . The assumptions and development of the N i e l s e n model are giv e n by Nielsen(1978,1980), Kousholt(1980) and N i e l s e n and Kousholt(1980). Johns and Madsen(l982) p r o v i d e f u r t h e r e x p l a n a t i o n s , and a p p l i e d the model to d u r a t i o n of l o a d t e s t r e s u l t s . The N i e l s e n model i s founded upon the Dugdale B a r e n b l a t t model f o r a crack i n a t h i n p l a t e with an a p p l i e d t e n s i l e s t r e s s as the s t r e n g t h r a t i o (as i n the N i e l s e n model) (2-22) 0 = c0 \/ then from (2-19), (2-20), (2-21) and (2-22) (2-19) K (2-23) * 2 = 6 \/ ( 2 c 0 ) 24 T h i s r e s u l t seems reasonable i n that the stronger the p l a s t i c m a t e r i a l i n the r e g i o n of the crack t i p (a higher value f o r the p l a s t i c l i m i t s t r e s s c^) the lower the s t e p l e n g t h 6. T h i s r e s u l t a l s o i m p l i e s that the higher the short term s t r e n g t h , the l a r g e r the s t e p l e n g t h 6 ( f o r a constant * , ) . I f the s t r e s s r a t i o i s c o n s i d e r e d , i t can be seen that the higher the s h o r t term s t r e n g t h * 0 , the higher a must be to maintain the same s t r e s s r a t i o . T h e r e f o r e f o r two specimens loaded to the same s t r e s s r a t i o (but with d i f f e r e n t values of short term str e n g t h ) the specimen with the high short term s t r e n g t h w i l l a l s o have the l a r g e r s t e p l e n g t h 6 and w i l l f a i l sooner. From (2-19) i t can be seen that 6 i s a f f e c t e d by two opposing i n f l u e n c e s . F i r s t c\\, which i f i n c r e a s e d tends to decrease 6. T h i s i s because more energy i s absorbed i n the process of f a i l u r e and t h e r e f o r e the step l e n g t h i s s h o r t e r . Second the f r a c t u r e toughness K which i f i n c r e a s e d tends to i n c r e a s e 6. Because a high K value i n d i c a t e s high l e v e l s of s t o r e d s t r a i n energy i n the m a t e r i a l surrounding the crack, then each crack step must be longer so that f o r a constant value of a high value of energy Fc can be absorbed at each step. 25 2.7 Evidence fo r the N i e l s e n and Step-wise Models. 2.7.1 I n t r o d u c t i o n . For many years t e s t s on the creep, s t r e n g t h , and d u r a t i o n of l o a d p r o p e r t i e s of wood have been researched e x t e n s i v e l y , but mostly as separate t o p i c s . Research i n t o f r a c t u r e mechanics and d u r a t i o n of l o a d i n wood, does y i e l d c e r t a i n t r e n d s , i n s p i t e of the inherent v a r i a b i l i t y of wood o f t e n encountered. Moreover the N i e l s e n and step-wise models f i t these trends and serve to e x p l a i n the anomalies other r e s e a r c h e r s chose to d i s c o u n t or e x p l a i n i n vague terms. However one q u a l i f i c a t i o n must be made on t h i s statement. In no way can the N i e l s e n and step-wise models support the t r a d i t i o n a l , s t r a i g h t l i n e d u r a t i o n of load l i n e s as developed by Wood, C l o u s e r , Youngs and H i l b r a n d e t c . , which are c o l l a t e d and summarised by Pearson(1972). These l i n e s e x h i b i t behaviour f a r d i f f e r e n t from that proposed \u2022 by the N i e l s e n and step-wise models. For reasons more f u l l y e x p l a i n e d in Chapter 3 these summary r e s u l t s are regarded as n o n r e p r e s e n t a t i v e of the i n i t i a t i n g f a i l u r e mode of commercial lumber i . e . , i n t e n s i o n p e r p e n d i c u l a r to the g r a i n . The bending t e s t r e s u l t s summarised by Pearson i n c l u d e t e s t s on many s p e c i e s , with v a r y i n g moisture contents and t e s t c o n d i t i o n s . A l l of the t e s t s are undertaken using c l e a r m a t e r i a l (most of which have a c r o s s s e c t i o n a l area of 1 cm 2), the f a i l u r e mode of which i s u s u a l l y i n compression of the top f i b r e s . In t h i s case, these r e s u l t s can i n no way represent the d u r a t i o n of load 26 behaviour of commercial m a t e r i a l , because d i f f e r e n t f a i l u r e modes may have separate d u r a t i o n of l o a d c h a r a c t e r i s t i c s . For example, Schniewind and Pozniak(1971) found that no d u r a t i o n of l o a d e f f e c t e x i s t s f o r c r a c k s propagating i n the t a n g e n t i a l r a d i a l plane. 2.7.2 Experimental Evidence. The a p p l i c a b i l i t y of f r a c t u r e mechanics to wood was f i r s t i n v e s t i g a t e d by Atack e t . a l . ( 1 9 6 1 ) . L a t e r , P o r t e r ( l 9 6 4 ) a l s o found that a G r i f f i t h - t y p e r e l a t i o n s h i p e x i s t e d between the crack l e n g t h and the f r a c t u r e s t r e s s . Since then c o n s i d e r a b l e experimental work on f r a c t u r e mechanics i n wood, some concerned with d u r a t i o n of l o a d has been r e p o r t e d and i s o u t l i n e d below. Researchers continue a f t e r Pearson i n p l o t t i n g s t r a i g h t l i n e s through the l o g a r i t h m of time to f a i l u r e versus s t r e s s r a t i o p l o t s . T h i s i s i l l u s t r a t e d i n the paper by Schniewind and Centeno(1973), where both short and long d u r a t i o n t e s t s are c a r r i e d out on Douglas f i r i n t e n s i o n p e r p e n d i c u l a r to the g r a i n . A s i g n i f i c a n t d i f f e r e n c e i s noted between the slope of the s t r a i g h t l i n e s f i t t e d f o r the two d i f f e r e n t time domains. The ramp l o a d t e s t s with f a i l u r e times between 0.5 seconds and 100 minutes y i e l d e d a very f l a t l i n e on the d u r a t i o n of load p l o t . The constant l o a d t e s t s with f a i l u r e times between 45 minutes and 18 days (corresponding s t r e s s r a t i o s of 0.9 to 0.7) y i e l d e d a much steeper l i n e on the d u r a t i o n of l o a d p l o t . Refer to f i g u r e 4 f o r p l o t s of these r e s u l t s . T h i s i n c r e a s i n g slope 27 of the p l o t with time supports the p r e d i c t i o n of the N i e l s e n and step-wise models, as do the f i n d i n g s of the other r e s e a r c h e r s mentioned i n the f o l l o w i n g . In t e s t i n g unnotched Scotch Pine i n t e n s i o n p e r p e n d i c u l a r to the g r a i n Bach's(1975) data ( f i g u r e 5) c o u l d perhaps more a p p r o p r i a t e l y be f i t t e d to a curve of negative c u r v a t u r e , p r o v i d i n g a much b e t t e r f i t at high s t r e s s r a t i o s . Mindess B a r r e t t and Spencer (1979) found with bending t e s t s on Douglas f i r i n t e n s i o n p e r p e n d i c u l a r to the g r a i n that f r a c t u r e s t r e n g t h i n c r e a s e d with displacement r a t e . They noted that t h e i r r e s u l t s underestimated the s e v e r i t y of the d u r a t i o n of l o a d e f f e c t when compared with other d u r a t i o n of load data i n t e n s i o n p e r p e n d i c u l a r to the g r a i n . T h i s i s best e x p l a i n e d by the f a c t t h a t t h e i r times to f a i l u r e were between 0.5 seconds and one day, and they are comparing t h e i r data with that of Bach(l975), whose times to f a i l u r e were e s s e n t i a l l y between one hour and s i x months, y i e l d i n g a steeper l i n e . Mindess Nadeau and Barrett(1975,1976) found when t e s t i n g Douglas f i r in t e n s i o n p e r p e n d i c u l a r to the g r a i n that \"At long times the slopes (of the d u r a t i o n of l o a d p l o t s ) seem to i n c r e a s e c o n s i d e r a b l y . . . \" . Recent rese a r c h at the U n i v e r s i t y of B r i t i s h Columbia by Johns and Madsen(l982) has a l s o r e v e a l e d a negative c u r v a t u r e f o r d u r a t i o n of l o a d t e s t s i n bending on commercial m a t e r i a l . C o n t i n u i n g r e s e a r c h by F o s c h i and Barrett(1982) i s a l s o y i e l d i n g s i m i l a r behaviour i . e . , negative c u r v a t u r e . Thus the p r e d i c t i o n s of the N i e l s e n and step-wise models 28 are w e l l supported by the experimental evidence i n the p r o f e s s i o n a l l i t e r a t u r e . 2.7.3 Q u a l i t a t i v e Evidence. The e x p l a n a t i o n s of the behaviour of wood under d u r a t i o n of l o a d as t o l d by other r e s e a r c h e r s i n the f i e l d of crack propagation, propose the same g e n e r a l mechanisms and l o g i c as i s a p p l i e d i n the theory and development of the v i s c o e l a s t i c f r a c t u r e mechanics models. Kollman(1963) d e s c r i b e s f a i l u r e as a process of i n i t i a l submicroscopic y i e l d i n g , f o l l o w e d by growth of m i c r o s c o p i c deformation and c r a c k s , f i n a l l y l e a d i n g to macroscopic f a i l u r e . T h i s i s i l l u s t r a t e d by t e s t s at high s t r e s s e s , where i r r e g u l a r i t i e s i n creep curves are i n t e r p r e t e d as sudden s t r u c t u r a l changes. Debaise et a l . ( l 9 6 6 ) made s i m i l a r o b s e r v a t i o n s . By monitoring a c o u s t i c emissions of wood as i t f r a c t u r e d , they hypothesised three main phases of f r a c t u r e : flaw n u c l e a t i o n , flaw growth, and unstable f r a c t u r e . They proposed d i f f e r e n t crack growth mechanisms depending on the crack c o n d i t i o n s , as shown i n f i g u r e 6. As an o b s e r v a t i o n they noted emissions o c c u r r i n g f o r very low l e v e l s of s t r e s s (20% of the f a i l u r e s t r e s s ) . T h i s f i n d i n g supports the v i s c o e l a s t i c models which p r e d i c t some amount of damage (be i t ever so small) to occur, even at very low s t r e s s r a t i o s . 29 2.8 Summary. As presented i n t h i s Chapter, the assumptions and theory of the N i e l s e n and step-wise models are based upon the theory of v i s c o e l a s t i c f r a c t u r e mechanics. Moreover, the p r e d i c t i o n s of the models are supported q u a l i t a t i v e l y and q u a n t i t a t i v e l y by the contemporary r e s e a r c h i n t o d u r a t i o n of l o a d . As such, the N i e l s e n and step-wise models are a u s e f u l advance in p r o v i d i n g a framework w i t h i n which the d u r a t i o n of l o a d phenomenon can be understood and q u a n t i f i e d . 30 CHAPTER 3 EXPERIMENT DESIGN 3.1 I n t r o d u c t i o n . The o b j e c t of the experiments i s to study and attempt to understand the propagation of cra c k s i n wood. I t i s necessary to model the cra c k s e x i s t i n g i n commercial m a t e r i a l as c l o s e l y as p o s s i b l e , and observe t h e i r behaviour, so c o n c l u s i o n s can be obtained which remain r e l e v a n t to the r e a l design s i t u a t i o n s . T h i s chapter o u t l i n e s the important c o n s i d e r a t i o n s ( i n the o p i n i o n of the author) with regard to the s e l e c t i o n of a s u i t a b l e crack geometry, mode of f a i l u r e , specimen design and e x p e r i p e n t a l method. 31 3.2 Crack O r i e n t a t i o n and Propagation. Due to the a n i s o t r o p i c nature of wood, many d i s t i n c t planes of f a i l u r e are p o s s i b l e . Even w i t h i n a plane, a crack may propagate i n one or both of the t a n g e n t i a l d i r e c t i o n s . I t may a l s o f a i l i n one of three modes. Because of the l a r g e number of p o s s i b i l i t i e s , a r a t i o n a l e i s developed here which shows that the f a i l u r e mode i n t h i s experiment i s such that i t i s the most r e l e v a n t r e p r e s e n t a t i o n of the c r i t i c a l f a i l u r e mode i n commercial m a t e r i a l . Three modes of f a i l u r e ( f i g u r e 7) are p o s s i b l e . I t i s suggested here that the c r i t i c a l mode of f a i l u r e f o r commercial lumber i s i n t e n s i o n p e r p e n d i c u l a r to the g r a i n i n the opening mode. Bending f a i l u r e i n commercial lumber i s g e n e r a l l y i n i t i a t e d at the knots. A crack i n i t i a t e d at the knot, curves around the knot, and i s then observed to propagate l o n g i t u d i n a l l y . As can be seen from f i g u r e 8 the slope of g r a i n at knots undergoes c o n s i d e r a b l e change. Upon the a p p l i c a t i o n of a t e n s i l e s t r e s s , the l o n g i t u d i n a l f i b r e s of the wood become s t r e s s e d i n t e n s i o n . Because df the curva t u r e of these f i b r e s , l a t e r a l s t r e s s e s are i n t r o d u c e d . These s t r e s s e s are i n t e n s i o n p e r p e n d i c u l a r to the g r a i n , the weakest plane of f a i l u r e f o r wood. Thus a small crack i n the plane of the f i b r e s c l o s e to the knot w i l l be s t r e s s e d i n the opening mode. T h i s small crack c o u l d be i n i t i a t e d at knots or by a d e f e c t i n the wood f i b r e s , or by a n i s o t r o p i c shrinkage s t r e s s e s . Schniewind and others have pro v i d e d comparisons of the f r a c t u r e toughness i n the v a r i o u s planes and d i r e c t i o n s , as w e l l 32 as some d u r a t i o n of l o a d c h a r a c t e r i s t i c s . The f r a c t u r e toughness r e s u l t s of Schniewind and Centeno(1973) can be separated i n t o two c a t e g o r i e s , each with separate values of f r a c t u r e toughness. T e s t s where f r a c t u r e o c c u r r e d i n a plane p a r a l l e l to the l o n g i t u d i n a l d i r e c t i o n y i e l d e d f r a c t u r e toughness v a l u e s of approximately one seventh the values where propagation was a c r o s s the g r a i n . T h i s supports the concept that f r a c t u r e would n a t u r a l l y occur i n the weakest plane i . e . , i n the plane of the g r a i n as a l r e a d y e x p l a i n e d . In order f o r a crack i n a three dimensional medium to propagate i n one d i r e c t i o n , i t must a l s o propagate i n the p e r p e n d i c u l a r d i r e c t i o n i . e . , a penny shaped crack propagates i n two d i r e c t i o n s w i t h i n the one plane. Within the t a n g e n t i a l l o n g i t u d i n a l plane Schniewind(1977) found the l o n g i t u d i n a l d i r e c t i o n of propagation e x h i b i t s a much more s e r i o u s d u r a t i o n of l o a d e f f e c t than the r a d i a l d i r e c t i o n , due to l e s s \" b l o c k i n g or blunting\"- by the c e l l w a l l s f o r the l o n g i t u d i n a l case. T h i s i n d i c a t e s that t e s t s should be c a r r i e d out with the crack propagating l o n g i t u d i n a l l y . Wood i n bending can f a i l due to the formation of compression w r i n k l e s i n the compression zone. T h i s f e a t u r e however i s u s u a l l y c o n f i n e d to the behaviour of the high s t r e n g t h m a t e r i a l , because the t e n s i o n zone i s f r e e of d e f e c t s . The low s t r e n g t h m a t e r i a l , which i s the most important when c o n s i d e r i n g safe design s t r e s s e s , u s u a l l y f a i l s by l o n g i t u d i n a l c rack propagation i n the t e n s i o n zone. These f a i l u r e s are u s u a l l y i n i t i a t e d at knots and d e f e c t s where s t r e s s e s i n t e n s i o n 33 p e r p e n d i c u l a r to the g r a i n are induced. In order to o b t a i n the best specimen d e s i g n , the c o r r e c t , c h o i c e between two a l t e r n a t i v e f a i l u r e planes needs to be made. The c r a c k s c o u l d propagate i n e i t h e r the t a n g e n t i a l l o n g i t u d i n a l plane or the r a d i a l l o n g i t u d i n a l p l a n e . On a macroscopic l e v e l , many commercial boards i n bending are observed to f a i l i n the r a d i a l l o n g i t u d i n a l plane. However, on a c l o s e r examination of the i n i t i a l f a i l u r e s u r f a c e at the knot, i t i s observed that the f a i l u r e has been i n i t i a t e d i n the t a n g e n t i a l l o n g i t u d i n a l plane. T h e r e f o r e i t was decided to t e s t c r a c k s propagating l o n g i t u d i n a l l y i n the t a n g e n t i a l l o n g i t u d i n a l plane i n the opening mode. I t i s p o s t u l a t e d that, t h i s mode of f a i l u r e would be r e p r e s e n t a t i v e of the i n i t i a t i o n of f a i l u r e i n commercial m a t e r i a l . As o u t l i n e d i n S e c t i o n 5 . 3 . 3 , the t a n g e n t i a l l o n g i t u d i n a l plane y i e l d s the h i g h e s t creep r a t e of any of the creep planes, i n d i c a t i n g ( a c c o r d i n g to the p r e d i c t i o n of the N i e l s e n and step-wise models) that the d u r a t i o n of load behaviour w i l l be most c r i t i c a l i n t h i s p l a n e . Therefore by t e s t i n g t h i s mode of f a i l u r e , the most c r i t i c a l f a i l u r e mode f o r wood i s ach i e v e d . N o t i c e that the crack c o n d i t i o n s f o r the t e s t specimen are not f a r removed from those f o r , a crack i n an i n f i n i t e sheet. However f o r commercial m a t e r i a l , the d i r e c t i o n of propagation of the crack may change as the crack lengthens, thus changing the s t r e s s f i e l d as the crack t i p . Because commercial specimens have a l o t of inherent redundancy (cracks propagating i n the reg i o n s of highest s t r e s s w i l l propagate and f i n d themselves i n 34 re g i o n s of lower s t r e s s ) and t h e r e f o r e w i l l take a c o n s i d e r a b l y longer time to f a i l than do the sma l l t e s t specimens used i n t h i s study which have no redundancy at a l l . Once the crack i n the s m a l l t e s t specimens begins to propagate there i s no chance t h a t the s t r e s s f i e l d w i l l d i m i n i s h , i t only i n t e n s i f i e s a c c o r d i n g t o (5-1). I t i s t h e r e f o r e proposed that the t e s t specimen used does not r e p l i c a t e the d u r a t i o n of l o a d behaviour of commercial m a t e r i a l . However, because the c r i t i c a l f a i l u r e i n i t i t a t i n g modes of both are s i m i l a r , i t i s proposed that the t e s t specimen can be a p p l i e d as a model, always p r o v i d i n g a lower bound to the d u r a t i o n of l o a d behaviour of commercial m a t e r i a l , and that the d u r a t i o n of l o a d c h a r a c t e r i s t i c s of the t e s t specimens be r e f l e c t e d i n the d u r a t i o n of l o a d behaviour of commercial m a t e r i a l . 3.3 Specimen Development. There are many s u i t a b l e specimen geometries to choose from. T e s t s have been c a r r i e d out i n double t o r s i o n by Mindess Nadeau and Barrett(1975,1976). T h i s geometry however r e q u i r e s s o p h i s t i c a t e d apparatus f o r each specimen and i s t h e r e f o r e i n a p p r o p r i a t e to t e s t i n g l a r g e sample s i z e s , e s p e c i a l l y over a long d u r a t i o n . Schniewind(1977) i n v e s t i g a t e d the t e n s i l e s t r e n g t h and d u r a t i o n of l o a d e f f e c t s i n t e n s i o n p e r p e n d i c u l a r t o the g r a i n , u s i n g notched beams i n bending. The disadvantage of t h i s method l i e s i n the f a c t that the s t r e s s i n t e n s i t y i n c r e a s e s markedly as the crack propagates, making a n a l y s i s more 35 d i f f i c u l t . A l s o , the specimen i s not r e p r e s e n t a t i v e of a r e a l flaw i n wood as i t only c o n s i d e r s h a l f a c r a c k , and does not a l l o w f o r the time dependent e f f e c t of the m a t e r i a l surrounding the other h a l f . S i n g l e edge notched specimens encounter the same problem. However, i f the d u r a t i o n of l o a d behaviour of c r a c k s of the nature as modelled by the s i n g l e edge notch specimen was to be determined, then the use of t h i s specimen geometry would be most a p p r o p r i a t e . Even f o r t e s t specimens of wood which are prepared from the same board, i f one wants co n f i d e n c e i n the r e s u l t s many specimens are r e q u i r e d , and the v a r i a b i l i t y of s t r e n g t h w i t h i n the p o p u l a t i o n of each t e s t needs to be as low as p o s s i b l e . Time, space, apparatus and labour requirements, r e q u i r e the specimen to be of r e l a t i v e l y small dimensions. P r e l i m i n a r y t e s t s were conducted by c u t t i n g a 2\"x6\" board i n t o 6\" l e n g t h s , and s t r e s s i n g them i n t e n s i o n p e r p e n d i c u l a r to the g r a i n a f t e r i n s e r t i n g a c e n t r a l l y p l a c e d 1\" l o n g i t u d i n a l through crack i n the specimen. However because the loads r e q u i r e d to f a i l such specimens were c o n s i d e r e d to be too l a r g e and the number of specimens taken from each board too few, a much smaller specimen and crack l e n g t h was f i n a l l y chosen. Subseqently a specimen design which avoided the l i m i t a t i o n s of other specimen d e s i g n s was developed. The specimens are s m a l l , e a s i l y manufactured and loaded, with crack c o n d i t i o n s s i m u l a t i n g the c r i t i c a l c r a c k s of commercial m a t e r i a l . In a d d i t i o n t h i s specimen design proved very s u c c e s s f u l i n reducing the c o e f f i c i e n t of v a r i a t i o n to q u i t e low v a l u e s , f o r wood. A 36 r e c t a n g u l a r p r i s m a t i c specimen, with the t e n s i l e l o a d i n g p l a t e s on the small ends, and a through crack i n i t i a t e d c e n t r a l l y i n the l o n g i t u d i n a l t a n g e n t i a l plane was used. Refer to f i g u r e s 9, 10, 11 and 12 f o r a v i s u a l p r e s e n t a t i o n . 3.4 Apparatus. In order to t e s t l a r g e numbers of specimens simultaneously the apparatus used must be compact i n nature. The m a t e r i a l s used were inexpensive and u n s o p h i s t i c a t e d . Maximum use was made of the m a t e r i a l s a l r e a d y a v a i l a b l e at the Department of C i v i l E n g i n e e r i n g S t r u c t u r e s Laboratory ( l e a d weights, s t e e l , Glulam beams e t c . ) Three separate racks were b u i l t , a l l o w i n g a t o t a l of 110 specimens to be t e s t e d s i m u l t a n e o u s l y . Each specimen was suspended from a mounting a t t a c h e d to the top of the support beam. The f r e e lower end of the specimen was a t t a c h e d to ( t h e l o a d p o i n t of a l e v e r arm whose fulcrum was underneath the support beam. A l e a d weight of approximately 20kg was f i x e d to the a p p r o p r i a t e l o c a t i o n on the l e v e r arm to give a load u n d e r e s t i m a t i n g the f i n a l l o a d on the specimen. For a c l e a r e r p i c t o r i a l p r e s e n t a t i o n r e f e r to f i g u r e s 13, 14 and 15. In order to apply the exact amount of l o a d to the specimen a small weighed bag of sand was suspended from the end of the l e v e r arm. For the short term t e s t s the Department of C i v i l E n g i n e e r i n g Satec t e s t i n g machine NO.20GBN 1002 with the 2000 l b l o a d c e l l was used on speed c o n t r o l (10% medium) y i e l d i n g a ramp 37 l o a d f a i l u r e time of approximately 45 seconds. To c a l i b r a t e the l e v e r arms, a d i a l guage p r o v i n g r i n g c a l i b r a t e d a g a i n s t the Satec l o a d c e l l was used. In determining moisture c o n t e n t s , the oven and s c a l e s i n the Department of C i v i l E n g i n e e r i n g S o i l s Laboratory were u t i l i s e d . The c r o s s s e c t i o n a l area of the specimens was measured at the crack c r o s s s e c t i o n by v e r n i e r c a l i p e r s . 3.5 Specimen P r e p a r a t i o n In order to maintain s i m i l a r samples, the specimens were numbered a c c o r d i n g to t h e i r l i n e a l p o s i t i o n i n the board. By s e l e c t i n g specimens i n numerical order, the samples f o r t e s t i n g were e q u a l l y r e p r e s e n t a t i v e of the l e n g t h of the board. For example, f o r a simple t e s t with only one d u r a t i o n of l o a d t e s t and one short term c o n t r o l t e s t , the p o p u l a t i o n would be d i v i d e d i n t o two i d e n t i c a l groups of specimens; one to be t e s t e d immediately to give the short term s t r e s s d i s t r i b u t i o n of the p o p u l a t i o n and the other to be t e s t e d under constant s t r e s s f o r a long d u r a t i o n of time, over which the f a i l u r e times are recorded. I n d i v i d u a l specimen p r e p a r a t i o n c o n s i s t s of the f o l l o w i n g s t e p s . 1. Squaring the edges of the board i n the p l a n e r . 2. C l e a v i n g the 2x6 i n t o two 1x6's using a t a b l e saw. 3. P l a n i n g both halves to equal t h i c k n e s s . 4. C u t t i n g and numbering specimens at 1.5 inch i n t e r v a l s along 38 the two boards. 5. Marking the c e n t r a l hole p o s i t i o n and the waist or necked down re g i o n with a template and c u t t i n g out the necked region on a small band saw ( f i g u r e 12). 6 . D r i l l i n g the c e n t r a l and end ho l e s i n the specimen. 7. F i x i n g the s t e e l end p l a t e s i n p o s i t i o n by i n s e r t i n g the screws u s i n g an e l e c t r i c d r i l l . 8. I n i t i a t i n g the crack by hammering a small symmetrical spear of known width c o n s t r u c t e d from a brass rod and a razor blade, through the c e n t r a l hole ( f i g u r e 12). 9. Measuring and r e c o r d i n g the c r o s s s e c t i o n a l area at the crack plane. 10. The l o a d i n g arrangement and the t e s t procedure i s d e s c r i b e d i n the f o l l o w i n g s e c t i o n . 3.6 Test Procedure For the constant l o a d t e s t s , the l e v e l of a p p l i e d s t r e s s i s c r i t i c a l because i t c o n t r o l s the r a t e at which f a i l u r e s occur. Depending on the s t r e s s l e v e l , the t e s t w i l l vary i n i t s d u r a t i o n . Based on past experience and d e s i r e d t e s t performance a d e c i s i o n i s made as to the most s u i t a b l e s t r e s s l e v e l to app l y . The time r e q u i r e d f o r the completion of the t e s t i s very s e n s i t i v e to the l e v e l of a p p l i e d s t r e s s , t h e r e f o r e great care i s r e q u i r e d i n determining the optimum s t r e s s l e v e l . In order to lo a d the specimens to the chosen s t r e s s l e v e l , the c r o s s s e c t i o n i s f i r s t measured and the r e q u i r e d a x i a l l o a d 39 c a l c u l a t e d . The l e a d weight i s f i x e d i n the a s s i g n e d p o s i t i o n on the l e v e r arm, which i s then c a l i b r a t e d u s ing the proving r i n g . The specimen i s p o s i t i o n e d on the apparatus and g e n t l y loaded, with the balance l o a d (a weighed bag of sand) t i e d to the end of the l e v e r arm. The l o a d i n g time i s noted, and subsequently the f a i l u r e time (or otherwise) i s a l s o recorded. In the e a r l y stages of the t e s t s , p e r s o n a l monitoring of the t e s t and r e c o r d i n g of the f a i l u r e times was continuous. However, as the experiment progressed, the t e s t was l e f t unattended f o r i n c r e a s i n g d u r a t i o n s as the frequency of f a i l u r e s d e c l i n e d . I f one or more specimens f a i l e d w i t h i n one of these i n t e r v a l s , the f a i l u r e times were i n t e r p o l a t e d i n a l i n e a r manner. T h i s approach worked w e l l because the rate of f a i l u r e s i s approximately p r o p o r t i o n a l t o the l o g a r i t h m of time. A f t e r a t e s t had progressed f o r s e v e r a l weeks i t was only necessary to r e c o r d the f a i l u r e s every two days. 3.7 Data A n a l y s i s . The short term f a i l u r e s t r e s s e s f o r a p a r t i c u l a r crack c o n d i t i o n showed some spread, however much l e s s than f o r uncracked specimens with c o e f f i c i e n t s of v a r i a t i o n as low as 0.06. Therefore i t was necessary to propose a model r e p r e s e n t a t i v e of the d i s t r i b u t i o n of short term s t r e n g t h s . The Gaussian Normal D i s t r i b u t i o n was chosen, as i t seemed reasonable that the v a r i a t i o n i n short term s t r e n g t h was l a r g e l y due to random e c c e n t r i c i t i e s i n the p o s i t i o n s of the end p l a t e s and i n 40 the p o s i t i o n of the necked down r e g i o n , thus superimposing random bending moments over top of the a x i a l l o a d . The mean value and the standard d e v i a t i o n of the short term s t r e s s e s were c a l c u l a t e d . The W e i b u l l model i s o f t e n used to model the s t r e n g t h d i s t r i b u t i o n of commercial m a t e r i a l . T h i s model i s based upon the \"weakest l i n k \" p r i n c i p l e e.g., a long chain with many l i n k s has a higher p r o b a b i l i t y of f a i l u r e than does a short chain with fewer l i n k s . In t h i s experiment, the numerous very small c r a c k s i n the wood are not i n i t i a t i n g f a i l u r e . Rather, only one of the \" l i n k s \" i s being t e s t e d , because the crack l e n g t h which i n i t i a t e s f a i l u r e i s c o n t r o l l e d . T h e r e f o r e the a p p l i c a t i o n of the W e i b u l l model i s c o n s i d e r e d i n a p p r o p r i a t e i n t h i s study. A f t e r a specimen has f a i l e d under constant l o a d , i t i s necessary to determine i t s s t r e s s r a t i o so that the f a i l u r e can be recorded on the s t r e s s r a t i o versus time to f a i l u r e p l o t . Before the s t r e s s r a t i o can be c a l c u l a t e d the o r i g i n a l short term s t r e n g t h of the specimen needs to be estimated. T h i s i s determined by the method of ranking. Because the specimens i n a d u r a t i o n of l o a d t e s t f a i l i n a sequence, the f a i l u r e times of the specimens are ranked. Using the d u r a t i o n of load t e s t sample s i z e , ranking i s a l s o a p p l i e d to the Normal d i s t r i b u t i o n of short term s t r e n g t h s a l r e a d y determined. From t h i s a ranked l i s t of short term s t r e n g t h s i s ob t a i n e d . Each ranked f a i l u r e time i s then a s s i g n e d the short term s t r e n g t h of equal rank. For example, the f i r s t specimen to f a i l i n the d u r a t i o n of loa d t e s t i s as s i g n e d a short term s t r e n g t h equal to the lowest 41 s t r e n g t h specimen taken from the Normal d i s t r i b u t i o n of short term s t r e n g t h . By d i v i d i n g the value of the s h o r t term s t r e n g t h by the l e v e l of a p p l i e d s t r e s s , an estimate of the s t r e s s r a t i o i s determined f o r each specimen. The p l o t of s t r e s s r a t i o versus the l o g a r i t h m of time to f a i l u r e i s used e x t e n s i v e l y , as seen i n Chapter 2 where the r e s u l t s of other r e s e a r c h e r s are quoted. In subsequent chapters the r e s u l t s of t h i s study are a l s o presented i n t h i s manner. In most t e s t s no specimens broke on l o a d i n g . However, s e v e r a l specimens d i d f a i l as soon as the l o a d was a p p l i e d . These f a i l u r e s were recorded on the d u r a t i o n of l o a d p l o t s but were as s i g n e d a short time to f a i l u r e and p l o t t e d with a d i f f e r e n t symbol. At f i r s t i t may seem alarming t h a t t h a t even towards the end of the experiments, there does not seem to be any slowing i n the r a t e of f a i l u r e s . However i t must be r e a l i s e d that the time s c a l e i s a l o g a r i t h m i c one, and i f the r e s u l t s were p l o t t e d with a r e a l time a x i s , the c u r v a t u r e would not be n e g a t i v e , but p o s i t i v e , with very l i t t l e change i n s t r e n g t h at long l o a d i n g times. In c a l c u l a t i n g the s t r e s s r a t i o , a l t e r n a t i v e approaches c o u l d have been adopted. By u t i l i s i n g t h e . s h o r t term s t r e n g t h s of the s u r v i v o r s of the d u r a t i o n of l o a d t e s t s , the short term s t r e n g t h s of the specimens which f a i l e d d u r i n g the t e s t s can be c a l c u l a t e d . For example, i f the t e s t i s terminated at a time where only 50% of the specimens have f a i l e d , then 50% of the specimens w i l l be s u r v i v o r s and w i l l be ramp loaded to f a i l u r e . 42 The s t r e n g t h of these s u r v i v o r s may i n d i c a t e that the short term c o n t r o l e s t a b l i s h e d from the sho r t term c o n t r o l sample i s not the best one to represent the short term s t r e n g t h of the d u r a t i o n of l o a d t e s t sample. The a p p r o p r i a t e adjustment can then be made. In t h i s study t h i s approach was not adopted f o r two reasons. F i r s t , many of the t e s t s d i d not have a s i g n i f i c a n t number of s u r v i v o r s . Second, because some of the s u r v i v o r s may be damaged they can no longer be used to represent the short term s t r e n g t h d i s t r i b u t i o n of the o r i g i n a l sample. 3.8 Determination of Ts. Ts i s (as a l r e a d y mentioned) the time at which the crack begins to propagate l o n g i t u d i n a l l y , and s i g n i f i e s the beginning of phase 2. D i f f e r e n t approaches c o u l d have been taken in order to determine the l e n g t h of time spent in phase 2. Rather than monitoring l o n g i t u d i n a l crack growth v i s u a l l y , a d i f f i c u l t technique even with the a i d of the most s o p h i s t i c a t e d equipment, a d i f f e r e n t method was adopted. I t was decided to t r y and \" c a t c h \" specimens at the time when the c r a c k s are lengthening i . e . , the crack i s undergoing phase 2. By s t o p p i n g a d u r a t i o n of l o a d t e s t while there are numerous s u r v i v o r s , some of the s u r v i v o r s w i l l be \"caught\" i n phase 2, while the remainder w i l l s t i l l be i n phase 1. The s u r v i v o r s undergoing phase 2 w i l l have accumulated some damage i . e . , t h e i r c r a c k s w i l l have lengthened. By f a i l i n g a l l s u r v i v o r s i n a ramp loa d t e s t , the number of damaged s u r v i v o r s (and the extent of damage) can be determined, 43 because the damaged specimens w i l l f a i l at lower s t r e s s e s as p r e d i c t e d by the s t r e s s i n t e n s i t y equation (2-1). For example, a sample of 20 specimens i s shown i n f i g u r e 16. I f the constant s t r e s s i s removed a f t e r 8 specimens have f a i l e d , then i t can be seen that specimens 9 and 10 w i l l by t h i s stage have accumulated some damage, i f the Ts l i n e i s i n p o s i t i o n ( 1 ) . These two specimens w i l l t h e r e f o r e f a i l at reduced s t r e s s e s as shown i n f i g u r e 17. I f the Ts l i n e i s at p o s i t i o n (2) however, specimens 11 12 and 13 w i l l a l s o be expected to accrue some damage. Th e r e f o r e , the number of damaged specimens f i x e s the p o s i t i o n of one p o i n t on the Ts l i n e , i n r e l a t i o n to the Teat l i n e . The number of damaged specimens i s d e f i n i n g the amount of time being spent i n phase 2, t h e r e f o r e determining the r e l a t i v e p o s i t i o n s of the Ts and Teat l i n e s . From (2-17), the d i s t a n c e between the Ts and Teat l i n e s i s c o n t r o l l e d by the F (e) \/ ( 0 2 * 2 ) term. For a p a r t i c u l a r s t r e s s r a t i o 9 and value of F (e) d e f i n e d by the model and the creep parameters chosen, the only unknown parameter i s . By f i t t i n g the experimental r e s u l t s to (2-17), an estimate of can be determined, which in turn y i e l d s an estimate of a,. When r e f e r r i n g to t h i s experiment as the Ts experiment, i t should be remembered that the i m p l i c a t i o n s go f u r t h e r than j u s t d etermining Ts. In e s t i m a t i n g and commenting upon i t s v a l i d i t y , the d e t e r m i n a t i o n of Ts becomes very important i n p r o v i d i n g a f u r t h e r t e s t of the p r e d i c t i o n s of the v i s c o e l a s t i c f r a c t u r e mechanics models, as they p e r t a i n to the time dependant 44 f a i l u r e of wood. 3.9 E r r o r s The random e r r o r s i n t h i s experiment are s m a l l . The e r r o r in measuring the c r o s s s e c t i o n i s very small and l e s s than 1%. Small random e r r o r s c o u l d occur i n the reading of the Satec and in the reading of the d i a l gauge when c a l i b r a t i n g . I t i s estimated that the maximum e r r o r p o s s i b l e i n the l e v e l of a p p l i e d s t r e s s i s i n the order of l e s s than 2%. However due to the e c c e n t r i c i t i e s of end p l a t e s and of the specimens themselves, v a r i a b i l i t y o c c u r r e d i n the l e v e l of maximum s t r e s s i n the specimens. As d i s c u s s e d f u r t h e r i n S e c t i o n 5.2.2 the maximum s t r e s s s at the c r i t i c a l c r o s s s e c t i o n was 10% higher (on the average) than the nominal a p p l i e d s t r e s s . Confidence l i m i t s on the r e s u l t s w i l l be d e a l t with i n the d i s c u s s i o n . 45 3.10 Summary To simulate the most c r i t i c a l f a i l u r e mechanism o c c u r r i n g i n the low p e r c e n t i l e s of commercial m a t e r i a l , the f o l l o w i n g specimen geometry was deci d e d upon. The specimen c o n s i s t e d of a u n i a x i a l t e n s i l e specimen with a c e n t r a l l y p l a c e d through crack, p r o v i d i n g a low c o e f f i c i e n t of v a r i a t i o n f o r the short term s t r e n g t h . The plane of the crack was the t a n g e n t i a l l o n g i t u d i n a l plane and the d i r e c t i o n of propagation was l o n g i t u d i n a l . The a p p l i e d s t r e s s was i n t e n s i o n p e r p e n d i c u l a r to the g r a i n , s t r e s s i n g the crack i n the opening mode. The method of ranking was assumed, so that the short term s t r e n g t h s of a c o n t r o l t e s t (approximated to the Normal D i s t r i b u t i o n ) c o u l d be a s s i g n e d to the specimens of the constant l o a d t e s t which were ranked a c c o r d i n g t o t h e i r f a i l u r e times. By d i v i d i n g the short term s t r e n g t h by the l e v e l of a p p l i e d s t r e s s , the s t r e s s r a t i o f o r each specimen was c a l c u l a t e d . The s t r e s s r a t i o of each- specimen was p l o t t e d a g a i n s t the lo g a r i t h m of the time t o f a i l u r e i n the development of the d u r a t i o n of load p l o t s . The d u r a t i o n of l o a d behaviour of t h i s s m a l l t e s t specimen i s only expected to p r o v i d e a lower bound (worst case) to the behaviour of commercial m a t e r i a l , which because of the redundancy o c c u r r i n g a r o u n d the knots, tends to demonstrate an improved d u r a t i o n of l o a d performance. However, the d u r a t i o n of lo a d trends determined from the small t e s t specimens would s t i l l be expected t o r e f l e c t themselves i n the behaviour of commercial m a t e r i a l . 46 CHAPTER 4 RESULTS 4.1 I n t r o d u c t i o n . T h i s chapter g i v e s a b r i e f d e s c r i p t i o n of the purpose of the experiments and t h e i r r e s u l t s f o r experiment Nos 1 through 6 (as o u t l i n e d i n Appendix 1). A d e t a i l e d d i s c u s s i o n of the i m p l i c a t i o n s i s presented i n Chapter 5. At the commencement of t h i s t h e s i s , i t was planned that the comparison of specimens loaded i n a st e p f u n c t i o n manner ( r e f e r r e d to as c y c l i c l o a d i n g ) with specimens loaded c o n s t a n t l y , be the major f e a t u r e of the r e s e a r c h . However as the study progressed, t h i s emphasis changed markedly as an i n t e r e s t i n the v i s c o e l a s t i c f r a c t u r e mechanics models developed. T h i s change i n emphasis i s r e f l e c t e d i n the sequence of the experiments which are d e s c r i b e d i n the order i n which they were c a r r i e d out. 47 4.2 Experiment D e s c r i p t i o n s . 4.2.1 Experiment No.l, C y c l i c - 1 . Experiment No.1 served the purpose of comparing c y c l i c l o a d i n g (or i n t e r m i t t e n t l o a d i n g ) with constant l o a d i n g , i n order to determine i f the assumption of l i n e a r l y adding loaded times i s v a l i d . In p r a c t i c e , d e s i g n e r s only c o n s i d e r a l i n e a r a d d i t i o n of the loaded times as c o n t r i b u t i n g to the design d u r a t i o n of l o a d thus i g n o r i n g the time f o r which a member i s unloaded. The step f u n c t i o n c y c l e of 3 hours under l o a d followed by 3 hours unloaded was chosen f o r the f o l l o w i n g reasons. As t h i s was the f i r s t experiment, an i n i t i a l estimate of the d u r a t i o n of lo a d behaviour was d e s i r e d . T h e r e f o r e the t o t a l t e s t d u r a t i o n d i d not need to be very l o n g . In order to perform a s i g n i f i c a n t number of c y c l e s w i t h i n t h i s time a 3 hour c y c l e time was most a p p r o p r i a t e . T h i s c y c l e was performed 3 times each day, and at the end of the t h i r d l o a d i n g p e r i o d a 9 hour recovery p e r i o d was allowed i n order f o r the author to o b t a i n some s l e e p . A t o t a l of 20 c y c l e s was performed i n t h i s manner. The recovery p e r i o d of 3 hours was c o n s i d e r e d adequate, because at l e a s t 90% of the t o t a l creep recovery w i l l have occ u r r e d by t h i s time, a c c o r d i n g to Kass(l969) who c a r r i e d out creep and recovery t e s t s i n t e n s i o n p e r p e n d i c u l a r to the g r a i n . At t h i s e a r l y stage i n the experiments, the method of i n s e r t i n g the c e n t r a l crack had not been p e r f e c t e d . The razor 48 blade used i n t h i s experiment only protruded from one si d e of the brass rod to which i t was at t a c h e d . In order to i n i t i a t e the crack, i t was d r i v e n through the c e n t r a l hole twice, each time c u t t i n g out one h a l f of the cr a c k . Because of t h i s procedure, c o n t r o l over the crack l e n g t h was not as good as i n the subsequent experiments where double edged blades were manufactured and used. As can be seen i n f i g u r e 18, no marked d i f f e r e n c e i n behaviour was observed. Due to the small sample s i z e , experiment No.4 was c a r r i e d out at a l a t e r date i n order to improve the confidence of the r e s u l t . 4.2.2 Experiment No.2, Two Crack Lengths. Experiment No.2 was designed to t e s t the s t r e n g t h e f f e c t , as p o s t u l a t e d by the N i e l s e n and step-wise models i . e . , f o r two specimens loaded to the same s t r e s s r a t i o , but whose short term s t r e n g t h s are d i f f e r e n t , the times to f a i l u r e w i l l be d i f f e r e n t . The high s t r e n g t h specimens w i l l f a i l sooner than the low s t r e n g t h specimens. The p r e d i c t e d d i f f e r e n c e in behaviour becomes more pronounced at longer times. In order to ob t a i n two groups of specimens with d i f f e r e n t s h o r t term s t r e n g t h s , two samples were prepared from the same board. One sample had a crack of t o t a l l e n g t h 6.22mm and the other a t o t a l crack l e n g t h of 10.8mm. Accord i n g to the f r a c t u r e toughness equation (2-1) the small crack l e n g t h specimens w i l l f a i l at a higher s t r e s s . In order that the same s t r e s s r a t i o be 49 a p p l i e d to both samples, a higher l e v e l of s t r e s s i s a p p l i e d to the s h o r t crack l e n g t h specimens. In t h i s way, the behaviour of specimens with d i f f e r e n t s t r e n g t h s but loaded to the same s t r e s s r a t i o s , can be s t u d i e d i n order to t e s t the p r e d i c t i o n of the s t r e n g t h e f f e c t . In a n a l y s i n g experiment Nos 2 and 3, a method was employed which served to combine a l l of the short term s t r e n g t h r e s u l t s i n t o one p o p u l a t i o n . For each experiment, the d i f f e r e n t specimen groups had d i f f e r e n t crack l e n g t h s and s l i g h t l y d i f f e r e n t crack geometries. They t h e r e f o r e had s l i g h t l y d i f f e r e n t F(c\/b) f a c t o r s . F(c\/b) i s the f a c t o r which i s a p p l i e d to the s t r e s s i n t e n s i t y to compensate f o r the lack of an i n f i n i t e medium, as c a l c u l a t e d by Tada, P a r i s and Irwin(l973) ( f i g u r e 26). Refer a l s o to S e c t i o n 5.2.5 where the F(c\/b) f a c t o r i s d i s c u s s e d f u r t h e r . When the short term t e s t s were c a r r i e d out, the a c t u a l f r a c t u r e toughness ( i n c o r p o r a t i n g F(c\/b) ) was c a l c u l a t e d f o r each specimen and the Normal curve f i t t e d to the e n t i r e p o p u l a t i o n . The s t r e s s r a t i o was c a l c u l a t e d by d i v i d i n g the a p p l i e d s t r e s s i n t e n s i t y f a c t o r by the a c t u a l f r a c t u r e toughness, r a t h e r than by d i v i d i n g the a p p l i e d s t r e s s by the short term s t r e n g t h . By u t i l i s i n g t h i s method, the data p o i n t s changed l i t t l e , but the method of a n a l y s i s was more c o n s i s t e n t . T h i s experiment ( f i g u r e 19) showed only l i m i t e d s e p a r a t i o n f o r the data p o i n t s of the two crack s i z e s , f o r two reasons. F i r s t , the s t r e n g t h e f f e c t as p r e d i c t e d by the Madsen and Johns(!982) f i t of the N i e l s e n model was l a t e r found 50 e x p e r i m e n t a l l y to be l e s s s i g n i f i c a n t than expected. Work by Madsen and Johns i n d i c a t e d a more s i g n i f i c a n t s t r e n g t h e f f e c t because of a high a^\/Y value of approximately 82MPa f i t t e d to the N i e l s e n model (Y was an unknown f u n c t i o n of random v a r i a b l e s d e s c r i b i n g the c h a r a c t e r i s t i c s of the crack f o r any p a r t i c u l a r p i e c e of lumber). Second, the l e v e l of a p p l i e d s t r e s s was too h i g h , c ausing the experiment to terminate i n a time too short f o r the s t r e n g t h e f f e c t to become very apparent. T h i s was caused by the f a c t that the specimens from the board used i n experiment No.2 f a i l e d unexpectedly sooner than those taken from the board f o r experiment No.1. In s p i t e of these l i m i t a t i o n s the t r e n d of the data p o i n t s at long times i s i n agreement with the t r e n d as p r e d i c t e d by the N i e l s e n and step-wise models i . e . , the long crack l e n g t h specimens (low strength) s u r v i v e d the l o n g e s t when loaded to the same s t r e s s r a t i o . 4.2.3 Experiment No.3, Three Crack Lengths. Because of the l i m i t a t i o n s of experiment No.2 a l r e a d y mentioned, experiment No.3 was a l s o aimed at t e s t i n g the s t r e n g t h e f f e c t as given by the v i s c o e l a s t i c f r a c t u r e mechanics models. By t e s t i n g three samples of specimens, each taken from the same p o p u l a t i o n , each with a d i f f e r e n t crack s i z e (and t h e r e f o r e s t r e n g t h ) , the s t r e n g t h e f f e c t was i n v e s t i g a t e d . The three crack lengths ( t o t a l ) were 10.06, 6.22, and 3.86 mm. T h i s experiment ( f i g u r e 20) was a success i n a p p l y i n g the c o r r e c t l e v e l of a p p l i e d s t r e s s , which y i e l d e d an average time 51 to f a i l u r e of approximately 10 days. At the end of the t e s t where the s t r e n g t h e f f e c t i s most pronounced, the data p o i n t s of the three crack s i z e s separated out i n manner p r e d i c t e d by the N i e l s e n and step-wise models, i . e . , f o r the same s t r e s s r a t i o , the h i g h s t r e n g t h (small crack) specimens f a i l e d sooner than the medium crack specimens, which i n tu r n f a i l e d at s h o r t e r times than the l a r g e crack (low stre n g t h ) specimens. Because the use of a very small crack was employed, the short term t e n s i l e s t r e s s at f a i l u r e became q u i t e high, averaging 2.57MPa. T h i s caused some of the specimens ( i n a p r e l i m i n a r y t e s t ) t o f a i l at the screw conne c t i o n a t the end p l a t e . At t h i s stage of the r e s e a r c h the p r a c t i c e of w a i s t i n g or necking down of the specimens over t h e i r middle p o r t i o n s was i n t r o d u c e d f o r the more h i g h l y s t r e s s e d specimens, i n order t o a v o i d end f a i l u r e s . A l l f u r t h e r t e s t s used necked specimens. 4.2.4 Experiment No.4, C y c l i c - 2 . As a l r e a d y mentioned, experiment No.4 ( f i g u r e 21) was a repeat of experiment No.1, but using a d i f f e r e n t board and an i n c r e a s e d sample s i z e , i n order that i n c r e a s e d c o n f i d e n c e c o u l d be expressed i n the pre v i o u s r e s u l t . A c y c l e of 2 hours on and 4 hours o f f was made p o s s i b l e by the a s s i s t a n c e of h e l p e r s , each r e s p o n s i b l e f o r l o a d i n g and unloading 2 hours l a t e r . T h i s c y c l e was maintained c o n t i n u o u s l y , day and n i g h t . Some small v a r i a t i o n s occurred i n the d u r a t i o n of the recovery p e r i o d , but the d u r a t i o n of the 52 loaded time was w e l l monitored. T h i s experiment s u c c e s s f u l l y confirmed the p r e v i o u s r e s u l t of experiment 1, by demonstrating that specimens loaded c y c l i c a l l y g i v e the same d u r a t i o n of l o a d p l o t as specimens loaded c o n s t a n t l y , assuming only the t o t a l loaded time i s p l o t t e d . 4.2.5 Experiment No.5, Moisture T e s t . Experiment No.5 was aimed at i n v e s t i g a t i n g the i n f l u e n c e of moisture content on the d u r a t i o n of l o a d e f f e c t , and t e s t i n g the r e s u l t a g a i n s t that p r e d i c t e d by the v i s c o e l a s t i c f r a c t u r e mechanics models. In order to do t h i s , two d u r a t i o n of load experiments were c a r r i e d out, one wet and one dry, each with t h e i r own short term s t r e n g t h c o n t r o l . Both samples were subsets of a l a r g e r sample. The dry t e s t was conducted w i t h i n the atmosphere of the t e s t room, sub j e c t to s m a l l f l u c t u a t i o n s i n humidity and temperature. The wet specimens were s a t u r a t e d in water f o r one week, and i n order to maintain t h e i r high moisture content f o r the d u r a t i o n of l o a d t e s t , were wrapped i n f i l t e r paper and enclosed i n p l a s t i c bags with f r e e water i n the bottom. In t h i s manner the high moisture content of the specimens was s u c c e s s f u l l y maintained f o r the d u r a t i o n of the experiment. As can be seen i n f i g u r e 22, the wet specimens f a i l e d much sooner than the dry. The r e s u l t s i n d i c a t e t h a t the times to f a i l u r e f o r the wet specimens are approximately one order of magnitude sooner than f o r the dry specimens. 53 As d i s c u s s e d f u r t h e r i n S e c t i o n 5.2.2, the wet specimens became curved upon immersion i n water. The c u r v a t u r e was about an a x i s i n the l o n g i t u d i n a l t a n g e n t i a l plane, p o i n t i n g i n the l o n g i t u d i n a l d i r e c t i o n . The e c c e n t r i c i t i e s induced by t h i s c u r v a t u r e reduced the short term s t r e n g t h s of the wet specimens c o n s i d e r a b l y . However the e s t i m a t i o n of the s t r e s s r a t i o remains v a l i d because the short term s t r e n g t h c o n t r o l s were a l s o wet and curved and t h i s reduced value was used i n the c a l c u l a t i o n s . 4.2.6 Experiment No.6, Ts. The aim of experiment No.6 was to determine the p o s i t i o n of the Ts l i n e and determine T h i s aim has been more f u l l y d e s c r i b e d i n S e c t i o n 3.8. The t e s t c o n s i s t e d of 34 short term c o n t r o l specimens and 89 l o a d d u r a t i o n specimens, a l l with t o t a l crack lengths of 6.22mm. In order that the p o s i t i o n of the Ts p o i n t be determined most a c c u r a t e l y , the l e v e l of a p p l i e d s t r e s s i s very important. In p a r a l l e l with the s t r e n g t h e f f e c t , the s e p a r a t i o n of the Ts l i n e and the Teat l i n e become more s i g n i f i c a n t at longer times. T h e r e f o r e i n order that the specimens be loaded to the c o r r e c t l e v e l of a p p l i e d s t r e s s f o r an a p p r o p r i a t e t e s t d u r a t i o n (2 weeks), 10 of the constant l o a d specimens were p r e t e s t e d f o r 3 days before the complement of the specimens were loaded. The d e t e r m i n a t i o n of the t e r m i n a t i o n time of the constant l o a d experiment or o f f - l o a d time i s a l s o important i n the design 54 of a sound Ts experiment. The o f f - l o a d time was not determined at the commencement of the constant l o a d t e s t , but r a t h e r during the t e s t , where the best d e c i s i o n c o u l d be made i n l i g h t of the d u r a t i o n of l o a d c h a r a c t e r i s t i c s of the t e s t so f a r . E s s e n t i a l l y , the d e c i s i o n when to o f f - l o a d was made upon the b a s i s of s t r e s s r a t i o . On the one hand, the longer the d u r a t i o n of the experiment, the more d i s t i n c t becomes the d i f f e r e n c e between the Ts p o i n t and the Teat l i n e . On the other hand, i f o f f - l o a d i s delayed too long, the c o n f i d e n c e i n the s t r e s s r a t i o of the s u r v i v o r s begins to d i m i n i s h . In a d d i t i o n , i f the t e s t i s l e f t f o r too long, a l l of the s u r v i v i n g specimens may demonstrate damage i n which case the Ts p o i n t f a i l s to be d e f i n e d , because the t o t a l number of damaged s u r v i v o r s can not been determined. The r e s u l t s of t h i s experiment are i l l u s t r a t e d in f i g u r e s 23 and 24. As p r e d i c t e d by the N i e l s e n and step-wise models, many s u r v i v o r s from the d u r a t i o n of l o a d t e s t demonstrated c o n s i d e r a b l e damage, with two short term f a i l u r e s t r e s s e s as low as l.90MPa. Note that the weakest specimen i n the short term c o n t r o l t e s t of sample s i z e 34 ( f i g u r e 25) had a short term s t r e n g t h of 2.l8MPa, c o n s i d e r a b l y higher than the minimum value found i n the s u r v i v o r s . The d e t e r m i n a t i o n of the Ts p o i n t as given i n f i g u r e 23 was based upon the o b s e r v a t i o n that 20 s u r v i v i n g specimens i n c u r r e d damage ( f i g u r e 24), the 21st s u r v i v o r being p l a c e d to the r i g h t of the c o n t r o l l i n e . The s t r e s s r a t i o of the l a s t specimen (the 59th) to f a i l i n the d u r a t i o n of l o a d t e s t was 0.730. The 55 s t r e s s r a t i o of the 79th (59th p l u s 20) specimen was 0.704. 4.3 Summary T h i s chapter has served to pr o v i d e an o u t l i n e of the day to day c o n s i d e r a t i o n s , and r e s u l t s of the experiments performed. Each experiment c o n t r i b u t e d to a b e t t e r understanding of how best to design the next one. Thus the experimental method became more e f f i c i e n t , and b e t t t e r c o n t r o l was e x e r c i s e d over the experiments, so that they t e s t e d the a p p r o p r i a t e f e a t u r e s more p r e c i s e l y . 56 CHAPTER 5 DISCUSSION 5.1 I n t r o d u c t i o n T h i s chapter f i r s t e x p l a i n s the methods of a n a l y s i s a p p l i e d i n the p r e s e n t a t i o n of the r e s u l t s , and then d i s c u s s e s the creep f u n c t i o n used, and other reseach i n t o the phenomenon of v i s c o e l a s t i c creep. F o l l o w i n g i s a d e t a i l e d d i s c u s s i o n of a l l of the experiments performed i n t h i s study, i n c l u d i n g comments on the r e s u l t i n g i m p l i c a t i o n s . F i n a l l y , mention i s made of the c o n f i d e n c e which can be expressed i n the r e s u l t s , and the g e n e r a l l i m i t a t i o n s of the experiment. i 5.2 Experimental Method and A n a l y s i s . 5.2.1 The Normal D i s t r i b u t i o n In the experimental a n a l y s i s , a Normal curve was f i t t e d to the s h o r t term s t r e n g t h d a t a . By a p p l y i n g the assumption of ranking ( i . e . , the weakest specimen f a i l s f i r s t ) , t h i s model was used to determine the short term s t r e n g t h s of the constant load specimens. T h i s curve p r o v i d e d a good f i t to the mid-range 57 data, however the f u l l extent of the t a i l s of the curve are not r e a l i s e d by the experimental data ( f i g u r e 25). Thus when the s t r e s s r a t i o i s c a l c u l a t e d , the f i r s t one or two p o i n t s s l i g h t l y o v erestimate the s t r e s s r a t i o , while the l a s t few p o i n t s underestimate i t . T h i s was the only l i m i t a t i o n of using the Normal model. 5.2.2 F r a c t u r e Toughness The specimen design used i n t h i s experiment was an o r i g i n a l one. However a comparison of the f r a c t u r e toughness values obtained here can s t i l l be made with those of Schniewind and Centeno(1973) who used a d i f f e r e n t specimen. In t e s t i n g a notched bending specimen (D. F i r ) i n the t a n g e n t i a l l o n g i t u d i n a l plane with propagation i n the l o n g i t u d i n a l d i r e c t i o n , they obtained a f r a c t u r e toughness value of 410 kPa m1'2. F o l l o w i n g i s a l i s t of the f r a c t u r e toughness values obtained i n t h i s study from the specimens with a c e n t r a l l y p o s i t i o n e d c r a c k . 58 Expt No, T i t l e F(c\/b) \u00ab 0(MPa) 2c(nun) Frac.Toug.(kPa ml\/2) 1 C y c l i c - 1 1.05 1.923 11.0 270 2 Two Crack 1.05 1.908 10.8 260 2 Two Crack 1.02 2.578 6.22 260 3 Three Crack 1.05 2.043 10.06 257 3 Three Crack ' 1.02 2.470 6.22 244 3 Three Crack 1.05 3.260 3.86 254 4 C y c l i c - 2 1.04 2.472 6.22 250 5 M o i s t u r e , Wet 1.04 1.742 6.22 180 5 M o i s t u r e , Dry 1.04 2.417 6.22 250 6 Ts 1.04 2.465 6.22 250 N o t i c e that experiment No.2 y i e l d s c o n s i s t e n t f r a c t u r e toughness v a l u e s . Experiment No.3 shows however, a higher v a r i a b i l i t y i n the f r a c t u r e toughness v a l u e s . The reason that the wet specimens have such a low value, i s not due to a low s t r e n g t h , but rather to the f a c t that the specimens became curved upon immersion i n water. In order to determine the e f f e c t of t h i s c u r v a t u r e , a tensometer was a t t a c h e d to an uncracked specimen ( a l t e r n a t e l y to oppposing f a c e s ) and the specimen p u l l e d t o a s t r a i n e q u i v a l e n t to the breaking s t r a i n . From t h i s measurement i t was estimated that the e c c e n t r i c i t y i n the wet specimens was induc i n g a s t r e s s d i s t r i b u t i o n at the c r i t i c a l c r o s s s e c t i o n where the maximum s t r e s s was 150% of the nominal. A s i m i l a r t e s t on dry specimens i n d i c a t e d an i n c r e a s e over the nominal s t r e s s of 10% was reasonable. In determining the e f f e c t s of e c c e n t r i c i t y and specimen c u r v a t u r e , t h i s t e s t i n g was only approximate. Because 59 the specimens had v a r y i n g e c c e n t r i c i t i e s and c u r v a t u r e s , the va l u e s of 150% and 110% were estimates of the order of magnitude of the e f f e c t s o n l y . By a p p l y i n g these adjustments, the wet and dry values of f r a c t u r e toughness become almost i d e n t i c a l . T h i s r e s u l t i s i n keeping with the assumption that the f a i l u r e mechanism i n commercial m a t e r i a l i s i n t e n s i o n p e r p e n d i c u l a r to the g r a i n . Madsen(1973,1975) a l s o found no d i f f e r e n c e i n the s t r e n g t h of wet and dry m a t e r i a l at the lower q u a n t i l e s , where knots i n i t i a t e f a i l u r e i n t e n s i o n p e r p e n d i c u l a r to the g r a i n . 5.2.3 F i t of the Creep and L i m i t Strength Parameters The Clouser creep f u n c t i o n parameters \"a\" and \"b\" (2-5) can be used to f i t the models to the d u r a t i o n of load data , p o i n t s . In a p p l y i n g (2-17), these parameters have an e f f e c t upon the slope of the d u r a t i o n of lo a d p l o t , and a l s o upon the p o s i t i o n along the time a x i s , ( f i g u r e 27). For a low \"b\" value the d u r a t i o n of lo a d l i n e w i l l be f l a t t e r than f o r a high \"b\" va l u e . The \"a\" parameter c o n t r o l s the p o s i t i o n along the d u r a t i o n of loa d curve on the time a x i s . A high \"a\" value tends to d i s p l a c e the d u r a t i o n of lo a d l i n e to the l e f t . The \u00ab, c,, and must i n c r e a s e . T h i s i s achieved by de c r e a s i n g to 5.5Mpa. Thus i t becomes unclear as to which model one should use, the step-wise model with tf,=16 MPa or the N i e l s e n model with 5.5MPa, because both provide an adequate f i t to the experimental d a t a . In order to e s t a b l i s h an estimate of a lower bound f o r in a t e s t independent of the Ts experiment, a new experiment was performed. The idea was to t e s t high q u a l i t y m a t e r i a l without i n i t i a l c r a c k s and of very small c r o s s s e c t i o n a l area i n t e n s i o n p e r p e n d i c u l a r to the g r a i n . In t h i s way, the f a i l u r e s u r f a c e ( i n the l i m i t as the specimen becomes very small) c o u l d be assumed t o be t o t a l l y p l a s t i c , with the f a i l u r e s t r e s s approaching the p l a s t i c l i m i t s t r e n g t h As small flaws w i l l always e x i s t , however, t h i s method can only p r o v i d e a lower bound to the value of , assuming the 72 creep f u n c t i o n to remain c o n s t a n t . I t seems however that part of the spread of the data f o r d i f f e r e n t s t r e n g t h s c o u l d be a t t r i b u t e d to the e f f e c t of n o n l i n e a r creep at the higher l e v e l s of s t r e s s . Creep t e s t s by Fouquet(1979) on boards i n bending where the s t r e s s e s are p a r a l l e l to the g r a i n , \"...suggest that the r e l a t i o n between the creep deformation and a p p l i e d s t r e s s i s not n e c e s s a r i l y l i n e a r f o r s t r e s s l e v e l s higher than 4500psi (31.0MPa).\" N o t i c e that the maximum s t r e s s a p p l i e d i n the t e s t s by Madsen and Johns i s 3830psi (26.4MPa). F o s c h i and Barrett(1982) r e s u l t s , with t e s t s on 2\"x6\" boards i n bending, a l s o demonstrate a s e p a r a t i o n of the d u r a t i o n of l o a d curves f o r the d i f f e r e n t l e v e l s of a p p l i e d l o a d . 5.7 D e n s i t y E f f e c t . Although only one s p e c i e s was t e s t e d , c e r t a i n c h a r a c t e r i s t i c s of d u r a t i o n of load behaviour were observed. Notably, a d i s t i n c t i o n e x i s t e d between the d u r a t i o n of load behaviour f o r specimens s i m i l a r except f o r t h e i r d e n s i t i e s . In p a r t i c u l a r , the boards f o r experiment No.1 and experiment No.2 were of markedly d i f f e r e n t d e n s i t i e s , 600 and 400 kg\/m3 r e s p e c t i v e l y . The g r a i n o r i e n t a t i o n s were the same, but the d u r a t i o n of l o a d behaviours q u i t e d i s t i n c t . The high d e n s i t y m a t e r i a l s u r v i v e d f o r a much longer time than the low d e n s i t y m a t e r i a l . The f i t of the parameters can be seen as i n f i g u r e s 36 and 39, where a=0.29 i s f i t t e d f o r the high d e n s i t y m a t e r i a l , and a=0.56 f o r the lower d e n s i t y m a t e r i a l . The 73 e s s e n t i a l d i f f e r e n c e f o r these two experiments i s assumed to be in the creep f u n c t i o n , however the high d e n s i t y of the m a t e r i a l c o u l d a l s o i n d i c a t e a higher value of cy should be a p p l i e d . T h i s would a l s o tend to i n c r e a s e the time to f a i l u r e as r e q u i r e d . Because n e i t h e r v a l u e , which i n t u r n i m p l i e s a lower v a l u e . Conversely, i t i s p o s s i b l e that many of the f a i l e d specimens were of a higher short term s t r e n g t h than assumed by ranking, thereby y i e l d i n g a higher * J \/ \u2022 i \u2022 i r c i \/ \u2022 ri i y U o' oi \u2022 140 120 100 80 60 40 20 0 0.2 0.4 0.6 0.8 01.0 Deflection , inche6 Fig. 3\u2014Accumulative acoustic \u2022million! and load versus de-flection for flexure. O o o o in c o tn jn E UJ 1.0 .8 s 2 Creep in Flexure a 10000 1000 CO 100 \u00a7 o o 10 10 100 Time, Minutes Emissions at one minute represent the observed number after the start of loading. M a x i m u m load was reached in less tlia:i one minute. fig. 4\u2014Accumulative acoustic emissions and deflection versus time for creep in flexure. F i g . 6 R e s u l t s of Debaise et a l . d 9 6 6 ) 802\/Ptiysical Metallurgy Principles Oisplocemsnt of crock iurtocts Fig. 19.50 The three basic fracture modes. in these considerations is the thickness of the plate. In a thick plate, the large depth of metal parallel to the crack front tends to restrict plastic flow parallel to the crack. On the other hand, a crack in a thin plate does not feel this restriction. As a consequence, a crack that passes through a thin plate can draw in the plate The Three Modes of F a i l u r e . F i g . 8 Induced S t r e s s e s i n t e n s i o n p e r p e d i c u l a r to the g r a i n 96 F i g . 10 Mounted Specimen. 99 No 6 37mm Screws Steel Endplate Wood Specimen Necked Region Central Hole Through Crack Crack Initiator F i g . 12 Diagrammatical Specimen, and Crack I n i t i a t i o n , 100 Chain Specimen Beam Pivot Lever Arm <\u00b1 190 mm Lead Sandbag F i g . 13 Apparatus (Diagrammatical). 101 102 F i g . 15 Apparatus. 103 in KEY \u2022 Constant Load Falure 1 o Expected Failure Test Terminated\u2014\u2022>! Ts(2) Ts(1) *TCat Log^ Time to Failure F i g . 16 Ts Determination. c o fit c a> E o 8. to KEY \u2022 Constant Load Falure \u00ab Ramp Load Failure Short Term Stress Failure Stress F i g . 17 Ts Determination. 104 1.0 0.9 0.8 o *< or 0.7 to to LU \u00a30.6 to 0.5 0.4 i e x 0 X ox \u2014 ex \u2022 x ex O- X \u00a9- X O- X-\u2014 o- * \u00a9- X-O- X-X-O- X-O- X-o> X-o - x-\u2014 O- X-O- X-KEY: _ x Constant Loading L \u00bb Cyclic Loading _ Failed on Loading L \u00bb-,\u00bb. Survivor _ Crack = n mm -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 L0G l 0 TIME TO FAILURE - (hours) F i g . 18 Dur a t i o n of lo a d p l o t f o r experiment 1. 105 A 1.0 0.9 0.8 o or 0.7 h t n t o LU \u00a30.6 0.5 0.41 0 0 X ***** \u00bbx * X 0 X X X KEY' L \u2022 Crack = 6.22mm * Crack = 10.80 mm \u2022 i i \u2022 \u2022 \u2022 \u2022 i \u2022 \u2022 \u00ab \u2022 t \u2022 \u2022 \u2022 \u2022 \u00bb \u2022 \u2022 \u2022 \u2022 i i \u2022 \u2022 \u2022 \u2022 i \u2022 \u2022 \u2022 \u2022 i \u2022 \u2022 \u2022 \u2022 i \u2022 \u2022\u2022\u2022<\u2022\u2022\u2022\u2022 i > -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 LOG I O TIME TO FAILURE - (hours) F i g . 19 Duration of l o a d p l o t f o r experiment 2. 1 0 6 i 1.0 0.9 0.5 X X X X \u2022 x 0 \u2022 X \u2022 X S 0.8 b I lo X ac \\ 'I. O i 0.7 to t KEY crr\\c '\u2022 \u2022 Crack= 3.84mm i\u2014U.o ~ 1 \/ 1 o Crack=6.22mm 0 ^ \" X x Crack=10.03 mm -\u00ab.-o,* Failed on Loading V,*-,*- Survivor 0.4 Y , r . l i . . . . I . . . . i . . . . I . . . . i . . . . I . . . . i . . . . I . . . . i . . . . I . . . . i . . . . I -2.0 -1.0 0.0 1.0 20 3.0 4.0 L0G l 0 TIME TO FAILURE - (hours) F i g . 20 Duration of load p l o t f o r experiment 3. 107 i 1.0 0 X 0.9 \u2014 ft A 0.8 o % cr 0.7 -X \\ x * \u00b0. tO to LU \u00a3 0 . 6 - KEY: x \u2022 X \u2022 \u2014 \u2022 Constant Loading to x Cyclic Loading 0.5 \u2014 Failed on Loading +.\u00bb. Survivor 0.4 Crack= 6.22 mm -2.0 -1.0 0.0 1.0 20 3.0 4.0 LOG l o TIME TO FAILURE - (hours) F i g . 21 D u r a t i o n of l o a d p l o t f o r experiment 4. 108 1.0 0.9 -0 0.8 o -0 \u2022* 0 0 0 0 0 0 \u201e or 0.7 to to LU \u00a30.6 to X X KEY = \u2022 Dry 0 0 \u00b0 0 0-* o-X P-\\ X X-X-0.5 \u2014 \u00ab Wet -v\u00ab Failed on Loading 0.4 \u2022-,*- Survivor Crocks 6.22 mm 1. . . . 1 w -2.0 -1.0 0.0 1.0 20 3.0 4.0 LOG I O TIME TO FAILURE - (hours) F i g . 22 Dur a t i o n of l o a d p l o t f o r experiment 5. 109 { 1.0 0.9 \u2014 \u2022 \u2022 0.8 \u2022 \u2022 \u2022 \u2022 o or 0.7 '-\u2022 L O C O U J \u00a30.6 KEY-to \u2022 Failed During Test 0.5 \u2014 \u2022 Ts Point Crack = 6.22mm 0.4 -2.0 -1.0 0.0 1.0 20 3.0 4.0 LOG | 0 TIME TO FAILURE - (hours) F i g . 23 Du r a t i o n of l o a d p l o t f o r experiment 6. 110 F i g . 24 Ts (Expt 6) S u r v i v o r s t r e n g t h s . SHORT TERM STRESS MPa F i g . 25 Normal f i t to short term s t r e n g t h data, Expt 6. 1 12 T H E C E N T E R C R A C K E D T E S T S P E C I M E N A. Stress I n t e n s i t y Factor Kj = LOG 1 0 LOADED TIME (HOURS) x o T a n g e n t i a l L o n g i t u d i n a l Plane R a d i a l L o n g i t u d i n a l Plane F i g . 32 Creep parameters, Schniewind and Barrett(1972) , R e p l o t t e d Data, a=0.13, b=0.26. 118 1-01-Tcat \u2022 Failed During Test 0.5 [- * T s P o i n t [ Crack = 6.22mm 0.4 --2.0 -1.0 0.0 1.0 2.0 3.0 4.0 LOG I O TIME TO FAILURE - (hours) F i g . 33 Step-Wise f i t to Expt 6 ( T s ) , ff,=l6MPa, a=0.343, b=!\/5. 119 1.0 0.9 0.8 < o r 0.7 to to u \u00a30 .6 to 0.5 0.4 Teat KEY* Failed During Test Ts Point Crack = 6.22mm 1 -2.0 -1.0 0.0 1.0 20 3.0 4.0 LOG I O TIME TO FAILURE - (hours) F i g . 34 N i e l s e n f i t to Expt 6 (Ts), \u00ab1=55MPa, a=0.343, b=!\/5 120 t 1.0 0.9 - \u2022< 0.8 o OC 0.7 -0 0 * ' X LO LO LU \u00a30.6 LO e KEY: Dry v ft\u2014 0.5 X Wet -V\" t Failed on Loading 0.4 o-,x- Survivor Crack=6.22mm -2.0 -1.0 0.0 1.0 L0G l 0 TIME TO FAILURE -2.0 3.0 4.0 (hours) F i g . 35 Step-Wise F i t to Moisture t e s t , Expt 5, tf,=l6MPa, Dry; a = 0 .343, b=0.20. Wet; a=0.8l, b=0 . 15. 121 i.ol 0.9 0.8 < cr 0.7 t o t o LU o r r\u2014 LO 0.6 0.5 0.4 1 KEY\u00bb _ \u2022 Crack = 6.22 mm L * Crack = 10.80 mm \"\u2022 \u2022 \u2022 \u2022 i \u2022 \u2022 \u2022 \u2022 ' \u2022 \u2022 \u2022 \u2022 i \u2022 \u2022 \u2022 \u2022 * \u2022 \u2022 \u2022 \u2022 i \u2022 \u2022 \u2022 \u2022 * \u2022 \u2022 \u2022 \u2022 i \u2022 \u2022 \u2022 \u2022 1 \u2022 \u2022 \u2022 \u2022 i \u2022 \u00bb \u2022 \u2022 1 \u2022 \u2022 * \u2022 i * \u2022 \u2022 \u2022 1 * \u2022 \u2022 * i -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 LOG | 0 TIME TO FAILURE - (hours) F i g . 36 Step-wise f i t to Expt 2, *,=16MPa, a=0.29, b=l\/3. 122 1.0 0 . 9 0 . 8 o i 0 . 7 to to LU \u00a3 0 . 6 t o 0 5 0 . 4 K E Y ' \u2022 C r o c k = 3 . 8 4 m m o C r o c k = 6 . 2 2 m m \u00ab C r o c k = 1 0 . 0 3 m m \u2022\u2022,-0,* F a i l e d o n L o a d i n g \u2022 - , - . \u00bb \u2022 S u r v i v o r T e a t cr= 261,186.U54 MPa I I I I I 1 I . . . . I . . . . I . . . . I I I II l III II I \u00bb - 2 . 0 - U > 0 . 0 1.0 2J0 3 .0 L 0 G l 0 T I M E T O F A I L U R E - ( h o u r s ) 4 . 0 F i g . 37 Step-wise f i t to Expt 3, o-^ieMPa, a = 0.l82, b=l\/3. 123 i 1.0 0.9 0.8 o i 0.7 LO LO LU \u00a30 .6 to 05 0.4 KEY: \u2022 Crack= 3.84 mm o Crocks 6.22mm \u00ab Crocks 10.03mm >.-\u2022,\u2022\" Failed on Loading Survivor Teat O-=2.61,1B6,1J64 MPa . U d U L I . . . . I . . . . I . . . . I f . . . I . . . . i . . . . I . . . . I . . . . I . . . . I . . . . I -2X) -1.0 0.0 1.0 2J0 3.0 4.0 L0G, o TIME TO FAILURE - (hours) F i g . 38 N i e l s e n f i t to Expt 3, cr, = l6MPa, a=0.l82, b=1\/3. 124 I 1.0 X ^ - ^ 0 X 0.9 \u2014 0 X 0 X . Teat O - X \\ 0.8 o t t o- \\ x <>\u2022 \\ > o - X X o- x- \\ *>\u2022 \u00bb O - X-u . 0.7 to to \u00a30.6 to \u2022 KEY: x Constant Loading o Cyclic Loading \u00b0 - X-\u00bb \u2022 X-o \u00bb \u00b0 - X-0.5 ~\u00b0.\u00ab. Failed on Loading Survivor 0.4 Crack = 11 mm -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 L0G | O TIME TO FAILURE - (hours) F i g . 39 Step-wise f i t to Expt 1, tf,=16MPa, a=0.58, b=l\/3. 125 1.0 0.9 0.8 o cr 0.7 to to UJ \u00a3 0 . 6 to 0.5 0.4 \u2014 O o ^ X ^ ^ ^ 9 5 X Limits : KEY: \\ \\ \\ l ^ - \" T c a t \\ \\*\\ 0 '- \u2022 Constant Loading \\ v \\ L x Cyclic Loading T s - ^ \" ^ Failed on Loading - \u2022-,\u00bb, Survivor L Cracks 6.22 mm -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 L 0 G | 0 TIME TO FAILURE - (hours) F i g . 40 Step-wise f i t t o Expt 4, o-, = 16MPa, a = 0.47, b=1\/4. 126 1.0 0.9 '\u2022 \u2022 ^95% CONFIDENCE LIMITS (about the tr e n d l i n e ) 0.8 o > LU 0.7 - \u2022 TREND LINE LO LO Ld \u00a3 0 . 6 -K E Y -LO \u2022 Failed During Test 0.5 \u2014 \u2022 Ts Point 0.4 -2.0 -1.0 0.0 1.0 Z0 3.0 4.0 L O G I O TIME TO FAILURE - ( h o u r s ) F i g . 41 Confidence L i m i t s on the S t r e s s R a t i o . 127 APPENDICES Appendix 1 Test Data T h i s appendix l i s t s the t e s t data of experiments Nos 1 through 6. I t a l s o g i v e s b r i e f comments on the i n d i v i d u a l f e a t u r e s of each experiment. 128 Test Number 1 S t a r t i n g Date Nov 8th, 1981 Test T i t l e , S u b t i t l e C y c l i c - 1 , C y c l i c Crack Length, Hole Diameter (mm) 11, 4.12 Specimen Length (mm), F(c\/b) 37.8, 1.05 Board Number 1 De n s i t y (kg\/m 3) 590 Moisture Content % (Wet Volume) . . . . . . . 7.3 Temperature ( C e l c i u s ) 22 Short term t e s t sample s i z e 17 Mean, and Standard D e v i a t i o n (Mpa) . . . 1.923, 0.214 Load D u r a t i o n sample s i z e 21 Load D u r a t i o n S t r e s s L e v e l (MPa) 1.550 F a i l u r e s , S u r v i v o r s 6, 15 Comments: The s u r v i v o r f a i l u r e s t r e s s e s (MPa) are as f o l l o w s ; 2.32, 2.22, 1 .62, 1 .93,, 2.07, 2. 14, 2.25, 1 .80, 2.23, 2.35, 2.19, 2.27, 2.09, 2.19. T h i s t e s t was loaded to a constant s t r e s s l e v e l f o r p e r i o d s of three hours, and then allowed to recover f o r p e r i o d s of three hours before the next l o a d c y c l e was a p p l i e d . T h i s p a t t e r n was maintained f o r a t o t a l of twenty complete c y c l e s , (60 hours t o t a l loaded t i m e ) . The r a d i a l - t a n g e n t i a l plane was p a r a l l e l t o , but i n c l i n e d at 35 degrees to the plane of the end p l a t e s . 129 Test Number 1 S t a r t i n g Date Nov 8th, 1981 Test T i t l e , S u b t i t l e C y c l i c - 1 , Constant Crack Length, Hole Diameter (mm) 11, 4.12 Specimen Length (mm), F(c\/b) 37.8, 1.05 Board Number 1 Den s i t y (kg\/m 3) 590 Moisture Content % (Wet Volume) 7.3 Temperature ( C e l c i u s ) 22 Short term t e s t sample s i z e 17 Mean, and Standard D e v i a t i o n (Mpa) . . . 1.923, 0.214 Duration Load sample s i z e 21 Load Duration S t r e s s L e v e l (MPa) . . . j . . 1.582 F a i l u r e s , S u r v i v o r s 9, 12 Comments: The s u r v i v o r f a i l u r e s t r e s s e s (MPa) are as f o l l o w s ; 1.87, 2.13, 2.12, 1.93, 2.12, 2.12, 2.22, 2.43, 2.13, 2.06, 2.13, 2.26. The r a d i a l - t a n g e n t i a l plane was p a r a l l e l to, but i n c l i n e d at 35 degrees to the plane of the end p l a t e s . Note that t h i s t e s t was terminated at time equals 1580 hours. 130 Test Number 2 S t a r t i n g Date Nov 20th, 1981 Test T i t l e , S u b t i t l e Two S i z e , Large Crack Crack Length, Hole Diameter (mm) 10.8, 4.12 Specimen Length (mm), F(c\/b) 37.4, 1.05 Board Number 42 Den s i t y (kg\/m 3) 410 Mo i s t u r e Content % (Wet Volume) 10.5 Temperature ( C e l c i u s ) 22 Short term t e s t sample s i z e 11 Mean, and Standard D e v i a t i o n (Mpa) . . . 1.908, 0.093 Du r a t i o n Load sample s i z e 15 Load Duration S t r e s s L e v e l (MPa) 1.639 F a i l u r e s , S u r v i v o r s 15, 0 Comments: The r a d i a l - t a n g e n t i a l plane was p a r a l l e l t o , but i n c l i n e d at 40 degrees to the plane of the end p l a t e s . 131 Test Number 2 S t a r t i n g Date Nov 20th, 1981 Test T i t l e , S u b t i t l e Two S i z e , Small Crack Crack Length, Hole Diameter (mm) 6.22, 3.81 Specimen Length (mm), F(c\/b) 37.4, 1.02 Board Number 42 De n s i t y (kg\/m 3) 410 Mo i s t u r e Content % (Wet Volume) 10.5 Temperature ( C e l c i u s ) 22 Short term t e s t sample s i z e 11 Mean, and Standard D e v i a t i o n (Mpa) . . . 2.578, 0.161 Du r a t i o n Load sample s i z e 15 Load D u r a t i o n S t r e s s L e v e l (MPa) 2.338 F a i l u r e s , S u r v i v o r s 15, 0 Comments: The r a d i a l - t a n g e n t i a l plane was p a r a l l e l t o , but i n c l i n e d at 40 degrees to the plane of the end p l a t e s . 132 Test Number 3 S t a r t i n g Date Dec 20th, 1981 Test T i t l e , S u b t i t l e . . . . Three s i z e , Large crack Crack Length, Hole Diameter (mm) . . . . 10.06, 5.08 Specimen Length (mm), F(c\/b) 37.5, 1.05 Board Numbers 1 02, 1 03, 1 04, 1 05 Den s i t y (kg\/m 3) resp 460, 470, 560, 440 Moisture Content % (Wet Volume) 6.0 Temperature ( C e l c i u s ) 22 Short term t e s t sample s i z e 22 Mean, and Standard D e v i a t i o n (Mpa) . . . 2.043, 0.248 Dura t i o n Load sample s i z e 21 Load D u r a t i o n S t r e s s L e v e l (MPa) 1.559 F a i l u r e s , S u r v i v o r s 20, 1 Comments: The s u r v i v o r f a i l u r e s t r e s s was 3.124 MPa. The r a d i a l - t a n g e n t i a l plane was p a r a l l e l t o , but i n c l i n e d at 35 degrees t o the plane of the end p l a t e s f o r boards 103 and 104. For boards 102 and 105 the plane of the g r a i n was p a r a l l e l to the end p l a t e s . 133 Test Number 3 S t a r t i n g Date Dec 20th, 1981 Test T i t l e , S u b t i t l e . . . . Three s i z e , Medium crack Crack Length, Hole Diameter (mm) . . . . 6.22, 3.81 Specimen Length (mm), F(c\/b) 32.0, 1.02 Board Numbers 1 02, 1 03, 1 04, 1 05 D e n s i t y (kg\/m 3) resp 460, 470, 560, 440 Moisture Content % (Wet Volume) 6.0 Temperature ( C e l c i u s ) 22 Short term t e s t sample s i z e 22 Mean, and Standard D e v i a t i o n (Mpa) . . . 2.473, 0.303 Dura t i o n Load sample s i z e 22 Load D u r a t i o n S t r e s s L e v e l (MPa) 1.823 F a i l u r e s , S u r v i v o r s 18, 3 Comments: The s u r v i v o r f a i l u r e s t r e s s e s were 2.710, 3.079, and 2.641 MPa. The r a d i a l - t a n g e n t i a l plane was p a r a l l e l t o , but i n c l i n e d at 35 spacing of t e x t i s 2 degrees to the plane of the end p l a t e s f o r boards 103 and 104. For boards 102 and 105 the plane of the g r a i n was p a r a l l e l to the end p l a t e s . 134 Test Number 3 S t a r t i n g Date Dec 20th, 1981 Test T i t l e , S u b t i t l e . . . . Three s i z e , Small crack Crack Length, Hole Diameter (mm) . . . . 3.86, 1.91 Specimen Length (mm), F(c\/b) 25.0, 1.015 Board Numbers 1 02, 1 03, 104, 1 05 Density (kg\/m 3) resp 460, 470, 560, 440 Moisture Content % (Wet Volume) 6.0 Temperature ( C e l c i u s ) 22 Short term t e s t sample s i z e 11 Mean, and Standard D e v i a t i o n (Mpa) . . . 3.260, 0.308 Du r a t i o n Load sample s i z e 22 Load D u r a t i o n S t r e s s L e v e l (MPa) 2.572 F a i l u r e s , S u r v i v o r s 22, 0 Comments: The r a d i a l - t a n g e n t i a l plane was p a r a l l e l t o , but i n c l i n e d at 35 degrees to the plane of the end p l a t e s f o r boards 103 and 104. For boards 102 and 105 the plane of the g r a i n was p a r a l l e l to the end p l a t e s . 135 Test Number 4 S t a r t i n g Date Feb 26th, 1982 Test T i t l e , S u b t i t l e C y c l i c - 2 , C y c l i c Crack Length, Hole Diameter (mm) . . . . 6.22, 2.03 Specimen Length (mm), F(c\/b) . . . . 25.0, 1.04 Board Number 102 Density (kg\/m 3) resp 440 Moisture Content % (Wet Volume) 6.0 Temperature ( C e l c i u s ) 22 Short term t e s t sample s i z e 17 Mean, and Standard D e v i a t i o n (Mpa) . . . 2.472, 0.203 Duration Load sample s i z e 28 Load D u r a t i o n S t r e s s L e v e l (MPa) 1.90 F a i l u r e s , S u r v i v o r s 28, 0 Comments: T h i s t e s t was loaded to a constant s t r e s s l e v e l f o r p e r i o d s of two hours, and then allowed to recover f o r p e r i o d s of four hours f o r a t o t a l of 23 c y c l e s . Then f o r a f u r t h e r 3 c y c l e s at the c o n c l u s i o n of the t e s t , the p e r i o d was i n c r e a s e d such that the loaded time was 8 hours and the recovery time 16 hours. 136 Test Number 4 S t a r t i n g Date Feb 26th, 1982 Test T i t l e , S u b t i t l e C y c l i c - 2 , Constant Crack Length, Hole Diameter (mm) . . . . 6.22, 2.03 Specimen Length (mm), F(c\/b) . . . . 25.0, 1.04 Board Number 102 Den s i t y (kg\/m 3) resp 440 Moi s t u r e Content % (Wet Volume) 6.0 Temperature ( C e l c i u s ) 22 Short term t e s t sample s i z e 17 Mean, and Standard D e v i a t i o n (Mpa) . . . 2.472, 0.203 Du r a t i o n Load sample s i z e 27 Load D u r a t i o n S t r e s s L e v e l (MPa) 1.90 F a i l u r e s , S u r v i v o r s 27, 0 Comments: T h i s t e s t served as a c o n t r o l t e s t f o r the C y c l i c , C y c l i c - 2 t e s t . 137 Test Number 5 S t a r t i n g Date March 4th, 1982 Test T i t l e , S u b t i t l e M o i s t u r e , Wet Crack Length, Hole Diameter (mm) . . . . 6.22, 2.03 Specimen Length (mm), F(c\/b) . . . . 25.0, 1.04 Board Number 102 Density (kg\/m 3) resp 460 Moisture Content % (Wet Volume) 60.0 Temperature ( C e l c i u s ) 22 Short term t e s t sample s i z e 16 Mean, and Standard D e v i a t i o n (Mpa) . . . 1.742, 0.151 Dura t i o n Load sample s i z e 17 Load Du r a t i o n S t r e s s L e v e l (MPa) 1.13 F a i l u r e s , S u r v i v o r s 15, 2 Comments: The ramp f a i l u r e s t r e s s e s of the s u r v i v o r s were 1.697 and 1.719 MPa. 138 Test Number 5 S t a r t i n g Date March 4th, 1982 Test T i t l e , S u b t i t l e M o isture, Dry Crack Length, Hole Diameter (mm) . . . . 6.22, 2.03 Specimen Length (mm), F(c\/b) . . . . 25.0, 1.04 Board Number 102 D e n s i t y (kg\/m 3) resp 460 Moisture Content % (Wet Volume) 6.0 Temperature ( C e l c i u s ) 22 Short term t e s t sample s i z e 17 Mean, and Standard D e v i a t i o n (Mpa) . . . 2.417, 0.201 D u r a t i o n Load sample s i z e 18 Load D u r a t i o n S t r e s s L e v e l (MPa) 1.838 F a i l u r e s , S u r v i v o r s 13, 5 Comments: The ramp f a i l u r e s t r e s s e s of the s u r v i v o r s were 2.80, 2.91, 2.67, 2.34, and 2.80 MPa. 139 Test Number 6 S t a r t i n g Date May 1st, 1982 Te s t T i t l e . Ts Crack Length, Hole Diameter (mm) . . . . 6.22, 2.03 Specimen Length (mm), F(c\/b) . . . . 25.0, 1.04 Board Number 200 Den s i t y (kg\/m 3) resp 510 Mo i s t u r e Content % (Wet Volume) 8.1 Temperature ( C e l c i u s ) 22 Short term t e s t sample s i z e 34 Mean, and Standard D e v i a t i o n (Mpa) . . . 2.465, 0.150 Du r a t i o n Load sample s i z e . 89 Load D u r a t i o n S t r e s s L e v e l (MPa) 1.645 F a i l u r e s , S u r v i v o r s . 54, 35 Comments: The ranked f a i l u r e s t r e s s e s (MPa) of the s u r v i v o r s are as f o l l o w s : 1.90, 1.90, 2.05, 2.21, 2.22, 2.22, 2.23, 2.29, 2.31, 2.33, 2.35, 2.36, 2.38, 2.39, 2.40, 2.43, 2.46, 2.53, 2.61, 2.64, 2.68, 2.71, 2.71, 2.73. 140 Appendix 2 Volume E f f e c t As r e f e r r e d to i n S e c t i o n 5.3, small c l e a r specimens were t e s t e d i n a x i a l t e n s i o n i n the t a n g e n t i a l l o n g i t u d i n a l plane. In the f i g u r e A1 below, the r e s u l t s of t h i s t e s t are p l o t t e d on the f i g u r e a l r e a d y p l o t t e d by B a r r e t t ( 1 9 7 4 ) . The volume of 6mmx5mmxl0mm = 300mm3 = 0.005in 3, i s p l o t t e d a g a i n s t the average short term s t r e n g t h found of 9.2MPar or 1330psi. New Data P o i n t \/ t r h-_ 10 X P R E S E N T A L L O W A B L E WORKING S T R E S S (dry s e r v i c e condi t ion , normal load d u r a t i o n . ' t r a n s f o r m e d v a l u e s 'open s y m b o l : c l e a r m a t e r i a l s o l i d symbol : c o m m e r c i a l m a t e r i a l half sol id: c l e a r gl ued- la minated CSA-086) \u2022 *Thut,(1970) a Fox, (1974-1) w F o x . ( 1 9 7 4 - 2 ) A A M a d s e n , (1 972 ) O (Schn iewind and Lyon,(1973) \u00bb, Pet e r s o n , (1 9 7 3 ) ' -2 10 V -r-10 17 10 V O L U M E (IN.3) FIG. 3. Linear n-erossion equations relating strength to volume for uniformly loaded blocks of commercial and clem 1 >ouglas-fir. F i g . A1 Volume E f f e c t P l o t by Barrett(1974) 141 Appendix 3 F a i l u r e C r i t e r i o n . The f a i l u r e c r i t e r i o n assumed i n (2-6) i s not the only c r i t e r i o n which c o u l d be assumed. Other c r i t e r i a such as, Fc = k d 2 or Fc = k 2 d or o t h e r s , c o u l d be a p p l i e d , however these would no longer s a t i s f y the G r i f f i t h theory of crack p r o p a g a t i o n . The f a i l u r e c r i t e r i o n assumed (2-6) i n t h i s study was Fc = k d = k ( t 0 , A t ) d ( t 0 , A t ) By s u b s t i t u t i n g t h i s c r i t e r i o n , the Ts times of the N i e l s e n and step-wise models c o i n c i d e . T h i s f e a t u r e a l l o w s ready comparison of the two models when f i t t i n g them to the same experimental data. The f a i l u r e c r i t e r i o n chosen by Brincker(1982) was as f o l l o w s , Fc = k d , but where d i s such that Fc = k ( t 0 , A t ) ( 2 d ( t 0 , A t ) - d(t | 0,2At) ) T h i s c r i t e r i o n g i v e s a lower Ts value than the simpler c r i t e r i o n as assumed i n (2-6). In p r i v a t e correspondence with Mr B r i n c k e r , he i n d i c a t e d that the reason he chose t h i s c r i t e r i o n was because i t was based upon \"thermodynamic p r i n c i p l e s \" . In s p i t e of t h i s , the use of the simpler c r i t e r i o n was maintained, as i t i s i n agreement with the estimate of Ts as determined by N i e l s e n i n h i s development of the N i e l s e n model. 142 Appendix 4 Adjustment C a l c u l a t i o n s . Ths s t r e s s r a t i o i s d e f i n e d as \u00ab\/ i n order to get the c o r r e c t f i t . For the case of f i t t i n g the N i e l s e n model, the same procedure i s a p p l i e d . The onl y d i f f e r e n c e i s i n the form of the f u n c t i o n used i n the e s t i m a t i o n of the d u r a t i o n of phase 2. For 1 46 the N i e l s e n model, (Ts-Tcat) i s l a r g e r than the corresponding value i n the step-wise model because F(e) i s l a r g e r , given that \"a\", \"b\" and are the same. In order that the N i e l s e n model f i t the same data as the step-wise model, the s t r e n g t h r a t i o must be i n c r e a s e d , thereby d e c r e a s i n g ( T s - T c a t ) . By adopting the same procedure as f o r the step-wise model, a value of 0=0.45 was s u b s t i t u t e d , which gave a value of \u00abr,=5.5MPa. T h i s value a p p l i e d to the N i e l s e n model, f i t s the data p o i n t s d i s p l a c e d 19% to the r i g h t . T h i s appendix has served two f u n c t i o n s . F i r s t , the c a l c u l a t i o n s f o r the adjustments as a p p l i e d i n Chapter 5 are shown. Second, the appendix served t o demonstrate a f u r t h e r a p p l i c a t i o n to which the v i s c o e l a s t i c f r a c t u r e mechanics models can be put. In f r a c t u r e problems i n wood, i t would be uncommon to encounter a s i t u a t i o n where the boundaries of the region c o u l d be assumed as i n f i n i t e . P a r t i c u l a r l y important c o u l d be the case where the crack i s c l o s e t o , or has a l r e a d y impinged upon the boundary. F r a c t u r e mechanics can provide an estimate of the f a i l u r e l o a d i f the value of the f r a c t u r e toughness i s known. V i s c o e l a s t i c f r a c t u r e mechanics can provide an estimate of the d u r a t i o n of l o a d c h a r a c t e r i s t i c s of the c r a c k . Depending on the nature of the m a t e r i a l surrounding the c r a c k , the F(c\/b) f a c t o r s may tend t o a c c e l l e r a t e or d e c e l l e r a t e crack growth. By a d j u s t i n g the F(c\/b) f a c t o r s i n the same manner as has been a p p l i e d i n t h i s appendix, an estimate of the d u r a t i o n of load behaviour c o u l d be made. I t should be noted that the term 147 F(c\/b) i s r e a l l y an o v e r s i m p l i f i c a t i o n f o r cases other than the c e n t r a l through crack used i n the experiments of t h i s study. For other more complex c r a c k geometries, many more f a c t o r s other than the crack l e n g t h as r e l a t e d to the specimen l e n g t h are i n v o l v e d . However, the same p r i n c i p l e s w i l l a p p l y . 148 Appendix 5 A Step-wise Value f o r P l a s t i c Y i e l d S t r e s s Equation (2-19) r e q u i r e s f u r t h e r e x p l a n a t i o n . T h i s equation l i n k s the y i e l d s t r e s s \u00ab , to the ste p l e n g t h 6. I f the value of 6 i s determined by assuming an e l a s t i c medium as given by (2-2), then i t i s not p o s s i b l e to assume that a value of (a p l a s t i c y i e l d s t r e s s ) can a l s o be determined from the same model. T h i s i n a b i l i t y to r e l a t e 6 to *, because they each d e r i v e from d i f f e r e n t m a t e r i a l behaviours (one step-wise e l a s t i c and the other continuous e l a s t i c p l a s t i c ) would appear t o i n v a l i d a t e (2 -19). In a d d i t i o n , the concept of a d i s c o n t i n u o u s crack movement, w i t h i n a theory based on the c o n t i n u i t y of s t r e s s e s and displacements, a l s o needs f u r t h e r e x p l a n a t i o n . In a p p l y i n g the f o l l o w i n g r a t i o n a l e to the mechanics of the step-wise model, a r e l a t i o n s h i p between c , and 6 i s developed below. It i s necessary to take the m a t e r i a l i n the mouth of the crack t i p and d i s c r e t i z e i t i n t o segments of len g t h 6. By assuming that these elements each have a uniform s t r e s s and assuming a l s o that they continue to s a t i s f y e q u i l i b r i u m by f o l l o w i n g c l o s e l y the e l a s t i c s t r e s s d i s t r i b u t i o n , then the f o l l o w i n g s t r e s s d i s t r i b u t i o n i s proposed as i n f i g u r e A2 below. A l s o , the d i s c o n t i n u o u s crack movement of the step-wise model i s developed f u r t h e r . Element 1 w i l l f a i l f i r s t . I t w i l l f a i l at a s t r e s s of (the average e l a s t i c s t r e s s over the l e n g t h 6), then have lengthened by a d i s t a n c e 6. Because wood does not demonstrate p l a s t i c i t y but ra t h e r tends to be b r i t t l e at f r a c t u r e , elements 1 2 and 3 are assumed to conform to the e l a s t i c d i s t r i b u t i o n of 149 s t r e s s as shown. Herein l i e s the c e n t r a l d i f f e r e n c e between the Dugdale B a r e n b l a t t model and t h i s one. Dugdale assumes that elements 1 2 and 3 are continuous and that the m a t e r i a l i n t h i s r e g i on i s deforming p l a s t i c a l l y at a constant s t r e s s The model proposed i n f i g u r e A2 assumes t h a t the m a t e r i a l i n the mouth of the crack t i p remains e l a s t i c ( v i s c o e l a s t i c i n t h i s case) u n t i l f a i l u r e , and that f a i l u r e occurs segment by segment in a d i s c r e t e step-wise manner. T h i s approach shows that by averaging the e l a s t i c s t r e s s d i s t r i b u t i o n over a d i s t a n c e 6 from the crack t i p , that an estimate of can be determined a c c o r d i n g to (2-19). 150 F i g . A2 Step-wise model of the crack t i p . ","attrs":{"lang":"en","ns":"http:\/\/www.w3.org\/2009\/08\/skos-reference\/skos.html#note","classmap":"oc:AnnotationContainer"},"iri":"http:\/\/www.w3.org\/2009\/08\/skos-reference\/skos.html#note","explain":"Simple Knowledge Organisation System; Notes are used to provide information relating to SKOS concepts. 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