The Role Of Scaled Tests In Evaluating Models Of Failure Michael R. Wisnom

Complexity of behaviour Multiple failure mechanisms that may interact

Fitting experimental data with models Open hole tensile tests Average stress criterion with suitable parameters fits the experimental data very well

Different models may give similar fit Average stress criterionWeibull fit, m=5 Models should be based on representation of physical mechanisms controlling failure

Scaled Tests Stress distributions in fully scaled tests should be identical Failure stress not expected to change with size To predict size effect, model must capture mechanisms Scaled tests provide a challenge for analysis methods

Overview Examples of scaling behaviour that challenge failure models –Defect controlled failure – Weibull approach –Delamination controlled – Fracture mechanics –Stress gradient controlled failure –Complex interaction of failure modes Stringent test is to validate models on scaled tests with data derived from independent tests

Fracture mechanics scaling Failure by delamination is controlled by the amount of energy available Scaled tests show strong dependence on size E.g. scaled tension tests on unnotched quasi-isotropic laminates failing by delamination from free edge Wisnom, Khan, Hallett, 2008 Failure of IM7/8552 (45 m /90 m /-45 m /0 m ) s m=2

Fracture mechanics fit Simple fracture mechanics arguments indicate that doubling dimensions should reduce strength by root 2 Fits data very well

Notched fibre direction tension Fibre dominated compact tension tests Similar fracture toughness from baseline and specimens with 50% and 100% increase in in-plane area May not apply to other layups with delamination Laffan, Pinho, Robinson, Ianucci, 2010 T300/920 (90/0) 8 /90) s

Fibre direction tensile strength Tensile stress or strain criteria widely used Careful tests reveal a size dependence of strength Failure usually occurs at stress concentration at grips masking underlying size effects Tapered specimens with chamfered plies give gauge length failures Not to scale

Scaled unidirectional tensile tests IM7/8552 Small coupon 0.5 x 5 x 30 mm All dimensions scaled x 2 Wisnom, Khan, Hallett,

Weibull interpretation Strength controlled by defects Weibull statistical theory appropriate Weibull modulus m= 41

Applicability of Weibull approach Weibull approach fits data from a wide range of tests E.g. scaled four point bending tests and different length tension tests on E-glass / x10x1 mm 300x10x1 mm 100x10x1 mm 60x5x2 mm 120x10x4 mm 240x20x8 mm Not to scale

Fit of scaled tests Weibull approach with m=29 captures observed phenomena: Size effect in bending Size effect in tension Relation between tension and bending strength Wisnom and Atkinson, 1997a Weibull fit

Weibull fit for transverse tension Works well for other cases that are defect controlled E.g. transverse tension on different sized AS4/ Weibull modulus is a function of variability O’Brien & Salpekar, 1995 m = 12.2

Interlaminar shear Interlaminar shear also defect controlled Size effect consistent with Weibull modulus of 20.3 Tending towards a constant strength at small sizes Indication of transition in failure mode? Scaled specimens XAS/913 Wisnom, 1999

Interlaminar shear with cracks Three point bending test Short Teflon inserts of different lengths Might be expected to follow fracture mechanics scaling Strength Crack length

Interlaminar shear with cracks Fracture mechanics gives very high strength for short cracks Will a limit be reached based on material strength? Strength Crack length

Interlaminar shear with cracks Experimental results show transition: –Approaching fracture mechanics for longer cracks –Reaches upper bound strength for very short cracks FEA with cohesive elements correlates very well Strength limit Wisnom, 1996

Stress gradient effect Compressive strength in bending shows a strong effect of stress gradient Failure is due to shear instability at the micromechanical level With stress gradient, less stressed fibres support others E.g. scaled pin-ended buckling tests on T800/924 carbon-epoxy Wisnom, Atkinson and Jones, 1997

Weibull fit to data Fit looks good! m=16.8

Confirmation of stress gradient effect Pin-ended tests with different volume but same thickness give similar strengths Weibull indicates a significant drop in strength with size Wisnom, Atkinson and Jones, 1997

Confirmation of stress gradient effect Combined compression and bending tests show significant differences in strength Cannot be explained by Weibull approach Wisnom and Atkinson, 1997b

Modelling gradient effect Neither stress based nor fracture mechanics approaches can fit data Failure is due to instability Controlled by fibre alignment and shear stress-strain response Can analyse with non- linear model including: –Waviness –Non-linear shear –Fibre bending stiffness Wisnom, 1994

Correlation of scaling effect FE analysis of shear instability assuming 2º max. misalignment captures trend Wisnom, 1997 FE Scaled tests

Interacting failure mechanisms In many cases multiple mechanisms interact E.g. in notched tension there is splitting, delamination and fibre failure, which are all affected by scaling in different ways In-plane scaling of 4 mm thick IM7/8552 quasi-isotropic laminates (45/90/-45/0) 4s symmetric

In-plane scaling, dispersed plies Size effect due to interaction of splitting and delamination at the notch with Weibull scaling of fibre strength Pattern of splits at notch Hallett, Green, Jiang, Wisnom, 2009

Interaction of damage mechanisms Strength is fibre controlled Weibull scaling does not give large enough effect Splitting and delamination scale with specimen Need BOTH mechanisms Damage acts as multiplier on Weibull Shown by Korschot & Beaumont, 1991 Weibull scaling Test results

In-plane scaling, blocked plies Scaled specimens with same dimensions and layup but blocked plies show very different response symmetric Hallett, Green, Jiang, Wisnom, 2009 (45 4 /90 4 /-45 4 /0 4 ) s

Average stress criterion Works well for dispersed ply cases Completely wrong prediction for blocked plies Key difference is delamination behaviour Wisnom, Hallett and Soutis 2010

Delamination controls scaling Delamination is critical Initiates from the hole and free edge Joins up across width Ratio of ligament width to ply thickness is key scaling parameter Wisnom & Hallett, 2009

Modelling Approach Delamination elements Split elements Lines show potential splits within plies (superimposed) introduced in the FE model (LS-Dyna) Not to scale Interface elements for delamination and splitting Weibull approach for fibre failure

Correlation of in-plane size effects Models representing key mechanisms correlate well with scaled tests Failure mechanisms, trends and strengths all captured with identical input data In-Plane Scaling Factor Hallett, Green, Jiang, Wisnom, 2009 Dispersed Blocked

A note of caution Scaling of strength can be caused by other factors Effect of manufacturing –Different cure in thicker specimens –Different voidage, fibre waviness or other defects –Important to use consistent manufacturing processes Other phenomena not properly scaled –Stress concentrations at load introduction may dominate –May be more difficult to introduce load in thicker specimens

Scaled tests provide a challenge to failure models Range of different scaling behaviour: –Weibull where controlled by defects –Fracture mechanics –Stress gradient effect in compression –Interaction of different modes Key issue is to include the correct mechanism Stringent test is to validate models on scaled tests with data derived from independent tests Conclusions

References Kortschot M. T. Beaumont P. W. R. & Ashby M. F Damage mechanics of composite materials: III – prediction of damage growth and notched strength. Composites Science and Technology 40: Wisnom M. R The effect of fibre waviness on the relationship between compressive and flexural strengths of unidirectional composites. Journal of Composite Materials 28: T. K. O’Brien and S.A. Salpekar, Scale effects on the transverse tensile strength of graphite epoxy composites, Composite Materials: Testing and Design, Vol. 11, Ed. E. Camponeschi, ASTM International, Philadelphia, STP 1206, pp Wisnom M. R Modelling the effect of cracks on interlaminar shear strength. Composites Part A 27: Wisnom MR, Atkinson JA 1997a. Reduction in tensile and flexural strength of unidirectional glass fibre-epoxy with increasing specimen size. Composite Structures 38: Wisnom MR, Atkinson JA 1997b. Constrained buckling tests show increasing compressive strain to failure with increasing strain gradient. Composites Part A 28: Wisnom MR, Atkinson JA, Jones MI Reduction in compressive strain to failure with increasing specimen size in pin-ended buckling tests. Composites Science and Technology 57: Wisnom MR Compressive failure under flexural loading: effects of specimen size, strain gradient and fibre waviness. Int. Conf. on Composite Materials, Vol. V. Gold Coast, Australia, p Wisnom, M R Size effects in the testing of fibre-composite materials, Composites Science and Technology 59: Wisnom M R, Khan B, Hallett S R Size effects in unnotched tensile strength of unidirectional and quasi-isotropic carbon/epoxy composites, Composite Structures 84:21-28 Hallett S R, Green B, Jiang W-G, Wisnom M R An experimental and numerical investigation into the damage mechanisms in notched composites. Composites Part A 40:613–624 Wisnom MR, Hallett SR The role of delamination in strength, failure mechanism and hole size effect in open hole tensile tests on quasi-isotropic laminates. Composites Part A 40: M. J. Laffan, S. T. Pinho, P. Robinson and L. Iannucci 2010, Measurement of the in situ ply fracture toughness associated with mode I fibre tensile failure in FRP. Part II: Size and lay-up effects, Composites Science and Technology, 70: Wisnom MR, Hallett SR, Soutis C Scaling Effects in Notched Composites. Journal of Composite Materials 44: