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Does transverse and shear loading affect the compression strength of unidirectional CFC? A reply to Dr Hart-Smith
Designer's Corner Short contributions of less than 1000 words plus key illustrations are being invited, covering topical issues associated with the design and application of composites. Notable designers from a broad range of industries including aerospace, automotive, civil, bioengineering and recreational are encouraged to submit a contribution to this section. Communications may cover, but not necessarily be restricted to, the following subjects: •
novel and innovative concepts in composites design and fabrication;
•
economics issues and other impediments to the wider exploitation of composites;
selection approaches for the various available fibre architectures and processes;
•
choice of failure criteria used for establishing integrity of composite products;
•
•
effective concurrent engineering approaches.
Contributions will be subject to a rapid review and publication process. Prospective contributions, marked for the 'Designer's Corner', should be submitted to: Dr Keith T. Kedward, Department of Mechanical & Environmental Engineering, University of California, Santa Barbara, CA 93106, USA. Fax." 1(805) 893 8651
Does transverse and shear loading affect the compression strength of unidirectional CFC? A reply to Dr H a r t - S m i t h E.C. EDGE
(British Aerospace Defence, Military Aircraft Division, UK) Dr Hart-Smith, in two contributions to Designer's Corner L2 and a large number of other technical articles, for example at the recent ICCS/7 Paisley Conference3, has consistently maintained that 'it is scientifically incorrect to employ interaction failure models whenever the mechanism of failure or the critical constituent of the composite changes with the state of stress'. This riposte examines situations where the uniaxial unidirectional compressive strength of carbon fibre/polyester resin composites appears to depend critically on resindominated shear and transverse loading.
INTERACTION BETWEEN AXIAL COMPRESSION AND IN-PLANE SHEAR First let us consider the case of simultaneously applied compression and shear loading. Work at Warton 4, consisting of the testing of tubular specimens of +45 ° material under combined loading, suggested that such an interaction exists and tentative interaction formulae were deduced4,s. Unfortunately the number of tests performed was small. However, similar work recently performed at Cambridge under funding from the Defence Research Agency6 involved a much larger number of tests. The results are shown in Fig. 1. It will be observed that the measured axial compression strength drops as the applied shear stress increases. The kinking failure mode is shown in Fig. 2.
The observed behaviour appears to have a relatively simple explanation. Unidirectional compressive strength is critically dependent on the support offered to the fibres and the applied shear reduces this, leading to the fibres bowing or buckling at lower load levels than they would otherwise. A simple interaction formula of the form o-~ + Iv,21 = I ~, ru
(1)
is an adequate mathematical description of this phenomenon, o-1 is the compressive stress and 312 the shear stress, and or, and ru the respective ultimate strengths. Note that cru and r, relate to the tubular
°-
(fi_..
SldJOJns FIll
16 - -
~
Fdlurc+)
J 0
'
• !00
.SO (MPa)
Fig. 1 Variation of axial compressive strength of tubular specimens with applied remote shear stress. The theory is for a strain-hardening material
001 0 ~ , 3 6 1 / 9 4 / 0 2 0 1 5 9 - 0 6 O 1994 B u t t e r w o r t h - H e i n e m a n n Ltd COMPOSITES . V O L U M E 25 . N U M B E R 2 . 1994
159
19 -
I '"
i!i
Fig. 2 Schematic diagram of a microbuckle kink band in a long, aligned fibre composite
constructions used in these tests and may differ from the values appropriate for fiat laminates, as Swanson and Nelson have observed 7. An equivalent expression to (1) but in terms o f strains rather than stresses can be deduced, but is complicated by the non-linear stress/ strain relationship in in-plane shear of unidirectional material. Equation (1) differs somewhat from the expression deduced by Grant and Sanders 4,5from the earlier Warton testing, but this is explained by the inadequacy of the data available to them. Hart-Smith 3 has criticized these formulations but he seems to think that the loading mode is equivalent to the tension-compression biaxial loading of cross-ply and multiangular lay-ups 7. This is not the case as the Warton and Cambridge experiments coupled cr~ and r~2 stresses within the same ply. In the work of Reference 7 there were no such interactions at the ply level.
INTERACTION BETWEEN AXIAL AND TRANSVERSE COMPRESSION Let us now turn our attention to how unidirectional compressive strength is affected if a transverse compressive stress is simultaneously applied. This has been studied by Parry and Wronski 8,9, who used a unidirectional cylinder under combined axial compression and hydrostatic pressure. This test is in fact a triaxial one and, under axial compressive applied stress a a and hydrostatic pressure H, we have o"l O"a "~ H and o'2 = o"3 = H. Their tests results are shown in Fig. 3, from which it will be observed that the compressive failure stress increased from a value of 1.5 GPa at H = 0 to equal the tensile strength of the material system (2.0 GPa) at H = 270 MPa. (In the 90 ° compression test failure can be expected at this level of transverse loading.) =
Again the physical explanation seems intuitively obvious, as the increased transverse stress can be expected to inhibit fibre bowing and buckling. This concept is reinforced by the change in failure mode which Parry and Wronski observed at about H = 150 MPa, which they interpreted as a change from a mode dominated by matrix yielding to one dominated by fibre buckling. Two simple interaction formulae can be deduced, for different ranges of H, namely
160
COMPOSITES.
NUMBER
2. 1994
0
50
100
~STATIC
150 ~ E
200
250
300
(MNm"2)
Fig. 3 Compressive strength (principal stress) of 0.6 Vf carbon fibre-reinforced plastic under superimposed hydrostatic pressure
cr~ - 1 1500 + 0.6H
0 < H _< 150
(2)
and al = 1 1590 + 3.41H
150 < H <
270
(3)
It can be objected that Equations (2) and (3) are not strictly interaction formulae, unlike Equation (1) and the Tsai-Wu polynomial, and that these effects can be accommodated simply by increasing the fibre stress or strain allowables, as Hart-Smith suggests 3. However, the work of Parry and Wronski has shown the important influence of the stress state in the transverse direction on unidirectional strength, and by implication the weakness of the Hart-Smith approach in diverting attention away from it. Therefore when reliable biaxial compressioncompression test results are available, the strain at failure may prove to be significantly greater than the uniaxial value. We have, however, to remember that the Parry and Wronski technique applies compression in both transverse directions, and further testing is required to determine more precisely the effect of transverse compression in one direction only.
INTERACTION BETWEEN AXIAL COMPRESSION A N D TRANSVERSE TENSION The observed effect of transverse compression on the measured longitudinal compression unidirectional strength prompts speculation about what will be the effect of transverse tension. It is not possible to go into this matter in depth here (my calculations are available on request), but Hart-Smith must be aware that, in the biaxial tension-compression
test, the transverse tension strain in the compression ply at failure is well in excess of that required to fail a 90 ° coupon (typically by a ratio of about 2:1), even when it is assumed that failure occurs at 60% of the uniaxial level. This level of transverse tension strain will mean a reduction of the ply transverse stiffness to about 40% of the uncracked value. This in turn must represent a reduction in the support given to the fibres by the matrix. This mechanism may provide a better explanation of the apparent loss in compressive strength than that put forward by Hart-Smith 3, particularly as not many workers have reported fibre shear failures. There is also the question of how to interpret the uniaxial compression control result in the work of Swanson and Nelson 7, the authors offering a different view to that of Hart-Smith (compare Fig. 6 of Reference 7 with Fig. 22 of Reference 10). This critically affects the interpretation of the whole series of compression-tension results.
CONCL UDING REMA RKS Hart-Smith 3 correctly states that nearly all composite structures have so far been certified by test rather than analysis. This is not surprising, considering that, as he also tells us, less than 1% of such structures are governed by unnotched strength. The necessary models to obtain notched and damage tolerant data from unnotched properties, let alone unidirectional or constituent properties, simply did not exist. The Hart-Smith approach seems to be dominated by the 'realism' of this present empirical certification route. Its best role seems to lie in initial sizing calculations in conjunction with empirical notch and damage tolerance knockdown factors. While the unnotched laminate on an aircraft can and must be designed as far as possible to avoid loading combinations such as those shown in Fig. 1, it is not possible to do this in the critical region round, for example, a notch. The geometry and stress gradients, and above all the matrix-dominated through-thickness stresses induced by the in-plane loading discontinuities, mean that interactions of this type are largely unavoidable.
If we are to find a way out of this costly empirically based impassse, we need tools of greater theoretical depth. This is the basis of the current interest in micromechanical modelling, and why we are seeing renewed interest in phemonena such as interactions, features which HartSmith is so keen to dismiss from consideration.
REFERENCES 1 Hart-Smith, L. J. 'Should fibrous composite failure modes be interacted or superimposed?' Composites 24 (1993) pp 53 56
2 Hart-Smlth, L. J. 'An inherent fallacy in composite interaction failure curves' Composites 24 (1993) pp 523 524 3 Hart-Smith, L. J. 'The role of biaxial stresses in discriminating between meaningful and illusory composite failure theories' Composite Structures 25 (1993) pp 3 20 4 Sanders, R. C. and Grant, P. 'The strength of laminated plates under in-plane loading' BAe Warton Report no SOR(P)I30 (January 1982) 5 Anon'Failure criteria for an individual layer of a fibre reinforced composite laminate under in-plane loading' Engineering Sciences Data Unit (ESDU) Item 83014 (June 1986) 6 Fleck, N. A. Presentation to Workshop on Compressive Failure, Cambridge University Engineering Dept, July 1993
7 Swanson,S. R. and Nelson, M. 'Failure properties of carbon/epoxy laminates under tension-compression biaxial stress' Proc Third Japan US Conf on Composite Materials, Tokyo, 1986
8 Parry,T. V. and Wronski, A. S. 'Kinking and tensile, compressive and interlaminar shear failure in carbon fibre reinforced plastic beams tested in flexure"J Mater Sei 16 (1981) p 439 9 Parry,T. V. and Wronski, A. S. 'Kinking and compressive failure in uniaxially aligned carbon fibre tested under superposed hydrostatic pressure' J Mater Sci 17 (1982) p 3656 10 Hart-Smith, L. 3. 'A scientific approach to composite laminate strength prediction' Douglas Paper 8467. Presented to lOth A S T M Symp on Composite Materials: Testing and Design, San Fransisco, CA, USA. April 1990
AUTHOR Mr Edge is a Specialist in Composites in the Structures Unit (postcode W310C) of British Aerospace Defence, Military Aircraft Division, Warton Aerodrome, Preston PR4 lAX, UK.
The difference between real and imaginary interactions in composite failure predictions. A reply to Mr Edge L. J. HART-SMITH (McDonnell Douglas Corporation, USA) The author is indebted to Mr Edge, of British Aerospace, for starting the open debate he has sought for so long over composite failure theories. He hopes that others will now participate, too. Whether or not the author is 100%
correct in the failure model he has proposed for fibre/ polymer composites, there can be no doubt that examples he has cited have exposed a need for major changes in what is currently taught on this subject.
C O M P O S I T E S . N U M B E R 2 . 1994
161
novel and innovative concepts in composites design and fabrication;
•
economics issues and other impediments to the wider exploitation of composites;
selection approaches for the various available fibre architectures and processes;
•
choice of failure criteria used for establishing integrity of composite products;
•
•
effective concurrent engineering approaches.
Contributions will be subject to a rapid review and publication process. Prospective contributions, marked for the 'Designer's Corner', should be submitted to: Dr Keith T. Kedward, Department of Mechanical & Environmental Engineering, University of California, Santa Barbara, CA 93106, USA. Fax." 1(805) 893 8651
Does transverse and shear loading affect the compression strength of unidirectional CFC? A reply to Dr H a r t - S m i t h E.C. EDGE
(British Aerospace Defence, Military Aircraft Division, UK) Dr Hart-Smith, in two contributions to Designer's Corner L2 and a large number of other technical articles, for example at the recent ICCS/7 Paisley Conference3, has consistently maintained that 'it is scientifically incorrect to employ interaction failure models whenever the mechanism of failure or the critical constituent of the composite changes with the state of stress'. This riposte examines situations where the uniaxial unidirectional compressive strength of carbon fibre/polyester resin composites appears to depend critically on resindominated shear and transverse loading.
INTERACTION BETWEEN AXIAL COMPRESSION AND IN-PLANE SHEAR First let us consider the case of simultaneously applied compression and shear loading. Work at Warton 4, consisting of the testing of tubular specimens of +45 ° material under combined loading, suggested that such an interaction exists and tentative interaction formulae were deduced4,s. Unfortunately the number of tests performed was small. However, similar work recently performed at Cambridge under funding from the Defence Research Agency6 involved a much larger number of tests. The results are shown in Fig. 1. It will be observed that the measured axial compression strength drops as the applied shear stress increases. The kinking failure mode is shown in Fig. 2.
The observed behaviour appears to have a relatively simple explanation. Unidirectional compressive strength is critically dependent on the support offered to the fibres and the applied shear reduces this, leading to the fibres bowing or buckling at lower load levels than they would otherwise. A simple interaction formula of the form o-~ + Iv,21 = I ~, ru
(1)
is an adequate mathematical description of this phenomenon, o-1 is the compressive stress and 312 the shear stress, and or, and ru the respective ultimate strengths. Note that cru and r, relate to the tubular
°-
(fi_..
SldJOJns FIll
16 - -
~
Fdlurc+)
J 0
'
• !00
.SO (MPa)
Fig. 1 Variation of axial compressive strength of tubular specimens with applied remote shear stress. The theory is for a strain-hardening material
001 0 ~ , 3 6 1 / 9 4 / 0 2 0 1 5 9 - 0 6 O 1994 B u t t e r w o r t h - H e i n e m a n n Ltd COMPOSITES . V O L U M E 25 . N U M B E R 2 . 1994
159
19 -
I '"
i!i
Fig. 2 Schematic diagram of a microbuckle kink band in a long, aligned fibre composite
constructions used in these tests and may differ from the values appropriate for fiat laminates, as Swanson and Nelson have observed 7. An equivalent expression to (1) but in terms o f strains rather than stresses can be deduced, but is complicated by the non-linear stress/ strain relationship in in-plane shear of unidirectional material. Equation (1) differs somewhat from the expression deduced by Grant and Sanders 4,5from the earlier Warton testing, but this is explained by the inadequacy of the data available to them. Hart-Smith 3 has criticized these formulations but he seems to think that the loading mode is equivalent to the tension-compression biaxial loading of cross-ply and multiangular lay-ups 7. This is not the case as the Warton and Cambridge experiments coupled cr~ and r~2 stresses within the same ply. In the work of Reference 7 there were no such interactions at the ply level.
INTERACTION BETWEEN AXIAL AND TRANSVERSE COMPRESSION Let us now turn our attention to how unidirectional compressive strength is affected if a transverse compressive stress is simultaneously applied. This has been studied by Parry and Wronski 8,9, who used a unidirectional cylinder under combined axial compression and hydrostatic pressure. This test is in fact a triaxial one and, under axial compressive applied stress a a and hydrostatic pressure H, we have o"l O"a "~ H and o'2 = o"3 = H. Their tests results are shown in Fig. 3, from which it will be observed that the compressive failure stress increased from a value of 1.5 GPa at H = 0 to equal the tensile strength of the material system (2.0 GPa) at H = 270 MPa. (In the 90 ° compression test failure can be expected at this level of transverse loading.) =
Again the physical explanation seems intuitively obvious, as the increased transverse stress can be expected to inhibit fibre bowing and buckling. This concept is reinforced by the change in failure mode which Parry and Wronski observed at about H = 150 MPa, which they interpreted as a change from a mode dominated by matrix yielding to one dominated by fibre buckling. Two simple interaction formulae can be deduced, for different ranges of H, namely
160
COMPOSITES.
NUMBER
2. 1994
0
50
100
~STATIC
150 ~ E
200
250
300
(MNm"2)
Fig. 3 Compressive strength (principal stress) of 0.6 Vf carbon fibre-reinforced plastic under superimposed hydrostatic pressure
cr~ - 1 1500 + 0.6H
0 < H _< 150
(2)
and al = 1 1590 + 3.41H
150 < H <
270
(3)
It can be objected that Equations (2) and (3) are not strictly interaction formulae, unlike Equation (1) and the Tsai-Wu polynomial, and that these effects can be accommodated simply by increasing the fibre stress or strain allowables, as Hart-Smith suggests 3. However, the work of Parry and Wronski has shown the important influence of the stress state in the transverse direction on unidirectional strength, and by implication the weakness of the Hart-Smith approach in diverting attention away from it. Therefore when reliable biaxial compressioncompression test results are available, the strain at failure may prove to be significantly greater than the uniaxial value. We have, however, to remember that the Parry and Wronski technique applies compression in both transverse directions, and further testing is required to determine more precisely the effect of transverse compression in one direction only.
INTERACTION BETWEEN AXIAL COMPRESSION A N D TRANSVERSE TENSION The observed effect of transverse compression on the measured longitudinal compression unidirectional strength prompts speculation about what will be the effect of transverse tension. It is not possible to go into this matter in depth here (my calculations are available on request), but Hart-Smith must be aware that, in the biaxial tension-compression
test, the transverse tension strain in the compression ply at failure is well in excess of that required to fail a 90 ° coupon (typically by a ratio of about 2:1), even when it is assumed that failure occurs at 60% of the uniaxial level. This level of transverse tension strain will mean a reduction of the ply transverse stiffness to about 40% of the uncracked value. This in turn must represent a reduction in the support given to the fibres by the matrix. This mechanism may provide a better explanation of the apparent loss in compressive strength than that put forward by Hart-Smith 3, particularly as not many workers have reported fibre shear failures. There is also the question of how to interpret the uniaxial compression control result in the work of Swanson and Nelson 7, the authors offering a different view to that of Hart-Smith (compare Fig. 6 of Reference 7 with Fig. 22 of Reference 10). This critically affects the interpretation of the whole series of compression-tension results.
CONCL UDING REMA RKS Hart-Smith 3 correctly states that nearly all composite structures have so far been certified by test rather than analysis. This is not surprising, considering that, as he also tells us, less than 1% of such structures are governed by unnotched strength. The necessary models to obtain notched and damage tolerant data from unnotched properties, let alone unidirectional or constituent properties, simply did not exist. The Hart-Smith approach seems to be dominated by the 'realism' of this present empirical certification route. Its best role seems to lie in initial sizing calculations in conjunction with empirical notch and damage tolerance knockdown factors. While the unnotched laminate on an aircraft can and must be designed as far as possible to avoid loading combinations such as those shown in Fig. 1, it is not possible to do this in the critical region round, for example, a notch. The geometry and stress gradients, and above all the matrix-dominated through-thickness stresses induced by the in-plane loading discontinuities, mean that interactions of this type are largely unavoidable.
If we are to find a way out of this costly empirically based impassse, we need tools of greater theoretical depth. This is the basis of the current interest in micromechanical modelling, and why we are seeing renewed interest in phemonena such as interactions, features which HartSmith is so keen to dismiss from consideration.
REFERENCES 1 Hart-Smith, L. J. 'Should fibrous composite failure modes be interacted or superimposed?' Composites 24 (1993) pp 53 56
2 Hart-Smlth, L. J. 'An inherent fallacy in composite interaction failure curves' Composites 24 (1993) pp 523 524 3 Hart-Smith, L. J. 'The role of biaxial stresses in discriminating between meaningful and illusory composite failure theories' Composite Structures 25 (1993) pp 3 20 4 Sanders, R. C. and Grant, P. 'The strength of laminated plates under in-plane loading' BAe Warton Report no SOR(P)I30 (January 1982) 5 Anon'Failure criteria for an individual layer of a fibre reinforced composite laminate under in-plane loading' Engineering Sciences Data Unit (ESDU) Item 83014 (June 1986) 6 Fleck, N. A. Presentation to Workshop on Compressive Failure, Cambridge University Engineering Dept, July 1993
7 Swanson,S. R. and Nelson, M. 'Failure properties of carbon/epoxy laminates under tension-compression biaxial stress' Proc Third Japan US Conf on Composite Materials, Tokyo, 1986
8 Parry,T. V. and Wronski, A. S. 'Kinking and tensile, compressive and interlaminar shear failure in carbon fibre reinforced plastic beams tested in flexure"J Mater Sei 16 (1981) p 439 9 Parry,T. V. and Wronski, A. S. 'Kinking and compressive failure in uniaxially aligned carbon fibre tested under superposed hydrostatic pressure' J Mater Sci 17 (1982) p 3656 10 Hart-Smith, L. 3. 'A scientific approach to composite laminate strength prediction' Douglas Paper 8467. Presented to lOth A S T M Symp on Composite Materials: Testing and Design, San Fransisco, CA, USA. April 1990
AUTHOR Mr Edge is a Specialist in Composites in the Structures Unit (postcode W310C) of British Aerospace Defence, Military Aircraft Division, Warton Aerodrome, Preston PR4 lAX, UK.
The difference between real and imaginary interactions in composite failure predictions. A reply to Mr Edge L. J. HART-SMITH (McDonnell Douglas Corporation, USA) The author is indebted to Mr Edge, of British Aerospace, for starting the open debate he has sought for so long over composite failure theories. He hopes that others will now participate, too. Whether or not the author is 100%
correct in the failure model he has proposed for fibre/ polymer composites, there can be no doubt that examples he has cited have exposed a need for major changes in what is currently taught on this subject.
C O M P O S I T E S . N U M B E R 2 . 1994
161