The Role Of Scaled Tests In Evaluating Models Of Failure

Michael R. Wisnom

www.bris.ac.uk/composites

Complexity of behaviour

Multiple failure mechanisms that may interact

Fitting experimental data with models

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Open hole tensile tests

Average stress criterion with suitable parameters fits the experimental data very well

Different models may give similar fit

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Average stress criterion Weibull fit, m=5

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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

(45m/90m/-45m/0m)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

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scaled x 2

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Wisnom, Khan, Hallett, 2008

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Weibull interpretation

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• 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 / 913

1000x10x1 mm

300x10x1 mm

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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 AS4/3501-6• 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?

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Wisnom, 1999

Interlaminar shear with cracks

• Three point bending test• Short Teflon inserts of different lengths• Might be expected to follow fracture mechanics scaling

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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?

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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

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Wisnom, Atkinson and Jones, 1997

Weibull fit to data

Fit looks good!

m=16.8

Confirmation of stress gradient effect

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)• 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 strength0

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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

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Weibull scaling

Test results

In-plane scaling, blocked plies

Scaled specimens with same dimensions and layup but blocked plies show very different response

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Hole diameter (mm)

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symmetricHallett, Green, Jiang, Wisnom, 2009

(454/904/-454/04)s

Average stress criterion

• Works well for dispersed ply cases • Completely wrong prediction for blocked plies• Key difference is delamination behaviour

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Experimental

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

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D (mm)

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Notched

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Unnotched w=4mm

Fit

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

1)( ElementsSolid of No Total

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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. 1991. Damage mechanics of composite materials: III –

prediction of damage growth and notched strength. Composites Science and Technology 40:147-165.• Wisnom M. R. 1994. The effect of fibre waviness on the relationship between compressive and flexural

strengths of unidirectional composites. Journal of Composite Materials 28:66-76.• T. K. O’Brien and S.A. Salpekar, 1995. 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. 23-52.

• Wisnom M. R. 1996. Modelling the effect of cracks on interlaminar shear strength. Composites Part A 27:17-24.

• Wisnom MR, Atkinson JA 1997a. Reduction in tensile and flexural strength of unidirectional glass fibre-epoxy with increasing specimen size. Composite Structures 38:405-412.

• Wisnom MR, Atkinson JA 1997b. Constrained buckling tests show increasing compressive strain to failure with increasing strain gradient. Composites Part A 28:959-964.

• Wisnom MR, Atkinson JA, Jones MI 1997. Reduction in compressive strain to failure with increasing specimen size in pin-ended buckling tests. Composites Science and Technology 57:1303-1308.

• Wisnom MR 1997. 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.683-692.

• Wisnom, M R 1999. Size effects in the testing of fibre-composite materials, Composites Science and Technology 59:1937-1957.

• Wisnom M R, Khan B, Hallett S R 2008. 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 2009. An experimental and numerical investigation into the damage mechanisms in notched composites. Composites Part A 40:613–624

• Wisnom MR, Hallett SR 2009. The role of delamination in strength, failure mechanism and hole size effect in open hole tensile tests on quasi-isotropic laminates. Composites Part A 40:335-342.

• 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, 70:614-621.

• Wisnom MR, Hallett SR, Soutis C 2010. Scaling Effects in Notched Composites. Journal of Composite Materials 44:195-210.