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
Notched/ unnotched
strength
Fitting experimental data with models
0.6
Open hole tensile tests
0.5
0.4
0.3
0.2
0
5
10
15
20
25
30
Hole diameter (mm)
Average stress criterion with suitable
parameters fits the experimental data very well
Notched/ unnotched
strength
Notched/ unnotched
strength
Different models may give similar fit
0.6
0.5
0.4
0.3
0.2
0
5
10
15
20
25
Hole diameter (mm)
Average stress criterion
30
0.6
0.5
0.4
0.3
0.2
0
5
10
15
20
25
Hole diameter (mm)
Weibull fit, m=5
Models should be based on representation of
physical mechanisms controlling failure
30
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
Failure of IM7/8552
(45m/90m/-45m/0m)s
m=2
Wisnom, Khan, Hallett, 2008
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
T300/920 (90/0)8/90)s
Laffan, Pinho, Robinson,
Ianucci, 2010
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
Tensile strength (MPa)
3000
• IM7/8552
• Small coupon
0.5 x 5 x 30 mm
2500
2000
1500
• All dimensions
scaled x 2
1000
500
0
1
1
2
2
3
4
4
8
Scale factor
Wisnom, Khan, Hallett, 2008
Weibull interpretation
Stress (MPa)
5000
• Strength controlled
by defects
• Weibull statistical
theory appropriate
2000
• Weibull modulus
m= 41
1000
50
500
5000
Volume (cubic mm)
50000
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
240x20x8 mm
120x10x4 mm
100x10x1 mm
Not to scale
300x10x1 mm
1000x10x1 mm
60x5x2 mm
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
Weibull fit
Wisnom and
Atkinson, 1997a
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
m = 12.2
O’Brien & Salpekar, 1995
Interlaminar shear
• Interlaminar shear also defect controlled
• Size effect consistent with Weibull modulus of 20.3
Interlaminar shear
strength (MPa)
• Tending towards a constant strength at small sizes
• Indication of transition in failure mode?
100
Scaled specimens
80
XAS/913
60
40
20
0
0
3
6
9
12
Thickness (mm)
15
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
Tensile Strength (MPa)
1000
800
600
400
200
0
0
1
Crack2 length 3
Scale factor
4
Interlaminar shear with cracks
• Fracture mechanics gives very high strength for
short cracks
• Will a limit be reached based on material strength?
Strength
Tensile Strength (MPa)
1000
800
600
400
200
0
0
1
Crack2 length 3
Scale factor
4
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
Strain at failure (%)
• With stress gradient, less
stressed fibres support
others
• E.g. scaled pin-ended
buckling tests on
T800/924 carbon-epoxy
2.5
2
1.5
1
0.5
0
1
2
8
Thickness (mm)
Wisnom, Atkinson and Jones, 1997
Weibull fit to data
Fit looks good!
m=16.8
Confirmation of stress gradient effect
Compressive strain at
failure (%)
• Pin-ended tests with different volume but same
thickness give similar strengths
• Weibull indicates a significant drop in strength with size
2
1.6
1.2
0.8
0.4
0
30x10x2
150x10x2
150x40x2
Specimen size (mm)
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 nonlinear model including:
– Waviness
– Non-linear shear
– Fibre bending
stiffness
Wisnom, 1994
Correlation of scaling effect
Scaled tests
FE
Wisnom, 1997
FE analysis of shear
instability assuming 2º
max. misalignment
captures trend
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
Strength (MPa)
500
Size effect due
to interaction
of splitting and
delamination
at the notch
with Weibull
scaling of fibre
strength
400
300
200
100
0
0
5
10
15
20
25
Hole diameter (mm)
Pattern of
splits at notch
Hallett, Green, Jiang, Wisnom, 2009
Interaction of damage mechanisms
Test results
Strength (MPa)
500
400
Weibull scaling
300
200
100
0
0
5
10
15
Hole diameter (mm)
20
25
• 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
In-plane scaling, blocked plies
Scaled specimens
with same
dimensions and
layup but blocked
plies show very
different response
500
Strength (MPa)
400
300
200
100
0
0
5
10
15
20
25
Hole diam eter (m m )
(454/904/-454/04)s
45
90
-45
0
Hallett, Green, Jiang, Wisnom, 2009
symmetric
Average stress criterion
• Works well for dispersed ply cases
• Completely wrong prediction for blocked plies
Notched/unnotched
strength
• Key difference is delamination behaviour
0.6
0.5
Average stress criterion
0.4
Experimental
0.3
0.2
0
5
10
15
20
25
Hole diameter (mm)
Wisnom, Hallett and Soutis 2010
Delamination controls scaling
Failure stress (MPa)
• Delamination is
critical
• Initiates from the
hole and free edge
500
450
400
350
300
250
200
150
100
50
0
Notched
Unnotched w=32mm
• Joins up across
width
• Ratio of ligament
width to ply
thickness is key
scaling parameter
Unnotched w=4mm
Fit
1
10
D (mm)
100
Wisnom & Hallett, 2009
Modelling Approach
Interface elements for
delamination and splitting
Split
elements
Delamination
elements
Weibull approach for fibre failure
Total No of Solid Elements
Not to
scale

i 1
(
i m
) Vi
o
 1
Lines show potential splits within
plies (superimposed) introduced
in the FE model (LS-Dyna)
Correlation of in-plane size effects
Dispersed
Blocked
• 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
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
Conclusions
• 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
References
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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.