A cumulative damage model to predict the fatigue life of composite laminates including the effect of a fibre-matrix interphase

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Int. J. Fatigue Vol. 17, No. 5, pp. 343-351, 1995 Copyright © 1995 Elsevier Science Limited Printed in Great Britain. All rights reserved (H42-1123/95/$10.00

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A cumulative damage model to predict the fatigue life of composite laminates including the effect of a fibre-matrix interphase S. Subramanian, K.L. Reifsnider and W.W. Stinchcomb Materials Response Group, Engineering Science and Mechanics Department, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA (Received 4 August 1994; revised 24 November 1994) Recent experimental efforts have established the significance of the fibre-matrix interface/interphase in the long-term behaviour of polymeric composites. Results indicate that small alterations at the interface level could translate into orders-of-magnitude changes in fatigue life. However, there is no model currently available in the literature to predict these changes. In this paper, a micromechanics model that includes the effects of the fibre-matrix interface is used in a simple cumulative damage scheme to predict the tensile fatigue behaviour of composite laminates. A new parameter called the 'efficiency of the interface' is used to model the degradation of the interface under fatigue loading. A rate equation that describes the changes in interfacial efficiency as a function of cycles is estimated using experimentally determined stiffness reduction data. The influence of this interfacial efficiency parameter on the tensile strength of unidirectional laminates is assessed using a micromechanics model. The effect of damage on the stiffness of the laminate is estimated by solving a boundary value problem associated with the particular damage mode (e.g. transverse matrix cracking). The fatigue life of the laminate is estimated by considering changes in stiffness due to creep and damage in the subcritical elements, and changes in strength associated with the critical element (0 ° ply). The influence of a fibre-matrix interface is included in the model by considering the degradation in the interface (interfacial efficiency) under fatigue loading. Changes in the interface property are used in the micromechanics model to estimate changes in the in-situ tensile strength of the 0° ply. The stress state and the strength of the 0° ply, calculated including the effects of damage, are then used in a maximum strain failure criterion to determine the fatigue life of the laminate. Predictions from this model are compared with experimental data. The predicted fatigue life and failure modes agree very well with the experimental data. (Keywords: fatigue; interface; damage; life prediction; composite laminate; micromechanics)

The fatigue behaviour of composite materials has been a subject of active research in recent years. The damage process in laminated composites subjected to fatigue loading is significantly different from that observed in conventional materials. Four main damage modes have been observed in laminated composites under fatigue loading: matrix cracking, fibre-matrix debonding, delaminations, and fibre fracture t,2. Typically, matrix cracking and delamination occur early in the life, while f i b r e - m a t r i x debonds and fibre fractures initiate during the beginning of the life and accumulate rapidly towards the end, leading to final failure 3. It has been observed that the stiffness of the laminate reduces during the process of damage accumulation in laminated composites 4.5. Reifsnider and Stinchcomb 6 have investigated the concept of using stiffness change as a non-destructive fatigue damage parameter. In general, they found that stiffness change can be quantitatively related to the fatigue life and residual strength of composite laminates through various models based on the observed microdamage. The analytical modelling of damage in composite

materials and the prediction of the degradation of properties under cyclic loading have received a great deal of attention in the last few years. Talreja 7, Allen et al. 8, and Joshi and Frantziskonis 9 have developed models based on internal variables, to predict damage accumulation under fatigue loading. N u m e r o u s semiempirical models have been proposed to predict the stiffness degradation and fatigue life of laminated composites. Lee and Daniels l° have used experimentally determined S - N curves for 0 ° and 90 ° laminates to predict the property degradation and fatigue life of cross-ply laminates. Hashin and R o t e m ~l assumed that failure could be described by a macroscopic failure function in terms of the applied load. The failure function contains unknown parameters, which are determined from simple experiments. The failure functions are dependent on the stress ratio, applied load frequency and cycles. Charewicz and Danieis ~2 have proposed a model based on the assumption that the rate of reduction of residual strength is a function of the life fraction. H a h n and Kim ~3 assumed that the residual strength reduction rate is inversely

343

344

S. Subramanian

proportional to the residual strength. Reifsnider and Stinchcomb 14 have proposed a critical element model, which assumes that the residual strength degradation rate is a power law function of the number of cycles and linearly dependent on the value of a failure function. Hwang and Han Ls have used the fatigue stiffness degradation in a maximum strain failure criterion to predict the life of composites. Liu and Lessard 16 have recently proposed a model that assumes damage degradation rates to be proportional to the applied stress and damage through a power law relationship. They have used the S - N curve of unidirectional material to estimate the constants in this relationship. Recently Reifsnider and Gao 17 and Subramanian et al. ts have proposed a micromechanicsbased approach to predict the fatigue life of unidirectional laminates. They have used a modified form of the M o r i - T a n a k a t9 method to estimate the stresses in the matrix and fibre phases. These are used in conjunction with the failure strengths of the matrix/ fibre phases in an appropriate failure criterion (Tsai-Hill or maximum stress type) to estimate the fatigue life of unidirectional laminates. None of these models explicitly considers the influence of the fibre-matrix interface. Recent experimental results 2°'2~ indicate that the region near the fibre surface, called the interphase, could possess elastic properties that are significantly different from those of the bulk matrix material. Small changes in properties of the interphase could lead to significantly altered fatigue performance. Swain -'1 and Subramanian et al. 2° have shown that by varying the local properties at the fibre-matrix interface level, the fatigue life can be altered significantly. They have also reported varied damage modes and failure mechanisms in cross-ply laminates, which have the same fibres and matrix, but different fibre-matrix interphases. In order to predict the fatigue response of these composites, a micromechanics-based model is appropriate. In this paper, a micromechanics model is used in conjunction with the critical element scheme ~ to predict the tensile fatigue life of laminated composites. The predictions from this model are compared with experimental results reported in ref. 22. D E S C R I P T I O N OF T H E M O D E L A cumulative damage scheme based on the critical element m o d e l proposed by Reifsnider and Stinchcomb 14 is used to predict the fatigue behavior of laminates. Figure 1 shows a schematic of the critical element model. In this model, the laminate is assumed to be composed of subcritical and critical elements. The primary load-carrying members (e.g. fibres at the fibre/matrix level, 0 ° ply at the lamina level) are normally the critical elements. The secondary, nonload-carrying members (e.g. matrix at the fibre/matrix level, off-axis plies at the lamina level) are called the subcritical elements. Non-catastrophic damage such as matrix cracking, local delaminations etc. is typically associated with subcritical elements. Strength of the laminate is associated with failure of the critical element. The reduction in stiffness as a function of cycles, caused by damage in the subcritical elements, is calculated by solving the boundary value problem associated with the specific damage mode. Using the

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reduced properties, the stress state in the critical element is calculated as a function of cycles. Reduction in the strength of the critical element as a function of cycles is typically estimated from the S - N curve of the 0 ° ply and from rate equations that describe any time-dependent degradation such as environmental attack. Knowing the stress state and strength of the critical element as a function of cycles, failure of the critical element is determined using a suitable failure criterion (maximum strain, Tsai-Hill etc. ). The fatigue life is estimated by calculating the number of cycles or time required for the failure of the critical element. The scheme described above has been used successfully in numerous earlier investigations 23"24 to predict the fatigue life of laminated composites. However, in this study, a micromechanics model described in ref. 22 is used in the above scheme to study the effects of the interface on the tensile fatigue behaviour of crossply laminates. This is done by varying a parameter associated with the fibre-matrix interface, as a function of cycles, and using a micromechanics model to estimate the effect of this change on the in-situ tensile strength of the 0 ° ply. It is well known that the static tensile strength of unidirectional laminates is related to fibre-matrix bonding. Numerous recent experimental efforts 2-',25,26 have demonstrated this effect clearly. The influence of the fibre-matrix interface on the tensile strength of unidirectional laminates has been predicted by many investigators using micromechanics models -'7.2~. Recently, Subramanian et al. 22 have introduced a new parameter called the efficien~;v o f the interface, 71, to predict the influence of the interface on the tensile strength of unidirectional composites. They have used two parameters to describe the interface: the interracial efficiency ~ and interfacial shear strength ri. Both of these parameters can be easily determined through simple experiments: namely, unidirectional tensile modulus measurement and single fibre fragmentation tests respectively. The interfacial efficiency determines how well the load is transferred from the matrix to the fibre. It is defined as the ratio between the

345

Fatigue life of composite laminates displacement in the fibre and the matrix at the interface region (7 -- Uf/Um). If the bonding is perfect and there is efficient load transfer from the matrix to the fibre, 7/--~ 1. If the bonding is imperfect and there is no load transfer from the matrix to the fibre then ~ ~ 0. In the tensile strength model, the stresses in the fibre and the matrix are determined using shear lag analysis. These stresses are used in an improved version of Batdorf's analysis L9 to predict tensile strength. Initiation of interfacial debonding is determined by comparing the average shear stress at the interface with the interfacial shear strength ri. The matrix is assumed to behave in an elastic-perfectly plastic manner. The model predicts the tensile strength and the failure mode (elastic/plastic) of the unidirectional composite. Failures accompanied by interracial debonding are called plastic failures while the stress-concentration-dominated failures with no interracial debonding are termed elastic failures. The micromechanics model shows that the tensile strength of a unidirectional laminate increases as 7/ reduces, when the failure is elastic (when there is no interracial debonding prior to final failure). However, when the failure is plastic (accompanied by interfacial debonding), the tensile strength reduces as T/reduces. This effect is shown in Figure 2. The transition from elastic to plastic failure results in a sharp increase in tensile strength. The authors 22 have described a simple scheme to determine the efficiency parameter 7/ using the experimentally measured tensile modulus of unidirectional laminates in a concentric cylinders model. Results indicate that as r/--~ 1 the modulus of the unidirectional laminate approaches the value predicted by the rule of mixtures, and as ~--* 0 it approaches the matrix modulus. Thus the interracial efficiency manifests itself in the form of a modulus reduction in unidirectional laminates. In this paper, the interfacial efficiency is used to represent changes in the interfacial bonding condition in the 0 ° ply of the laminate, under tensile fatigue loading. Since the interfacial efficiency is directly related to the modulus of the unidirectional laminate, O. 60 M ct o

Weibull shape factor for the fiber Weibull location parameter for the fiber

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where f t . , B,, P, are material constants, ~,pp is the applied external stress, (r,t,, is the static tensile strength and N is the fatigue life. Note that the static tensile strength of the 0 ° laminate is a function of the interracial efficiency parameter rl, and varies as a function of cycles. It is claimed that the constants in the tensile strength reduction curve of a unidirectional laminate are unaffected by changes in the interface. However, the in-situ tensile strength of the unidirectional laminate is influenced by the interracial bonding condition, which is characterized by two parameters: the interracial efficiency ~ and interracial shear strength "q. It is postulated that the interfacial bonding condition changes with cycles, in the 0 ° ply of the cross-ply laminate. Knowing the interfacial strength/efficiency degradation rate, the in-situ tensile strength of the unidirectional laminate can be estimated as a function of cycles using the micromechanics model described in ref. 22. This tensile strength is used in the S - N curve of the 0° ply to estimate the in-situ tensile strength of the 0° ply and the corresponding life, N, as a function of cycles. The influence of the interface on the tensile fatigue behaviour is characterized using different interfacial degradation rates in the 0 ° ply of the laminates in the micromechanics model. In this analysis, the degradation in interfacial strength is not considered. It is assumed that the changes in the interface can be represented completely by rate equations that describe the changes in the interfacial efficiency rt, under tensile fatigue loading.

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it is advantageous to use this parameter to describe the degradation of the interface under fatigue loading. The exact form of this degradation equation can be estimated from the stiffness reduction in the 0 ° ply of the laminate under cyclic loading. Knowing the interracial degradation rate (changes in interracial shear strength and/or efficiency) as a function of cycles, the influence of the interphase on tensile fatigue behaviour can be predicted using the critical element model in conjunction with the micromechanics model described in ref. 22. It must be mentioned here that the direct experimental determination of interfacial shear strength degradation as a function of cycles is difficult because most interfacial strength measurement tests require model composites. Also, there is no non-destructive testing technique currently available to estimate the degradation of interfacial strength under fatigue loading. Hence the use of a parameter such as interracial efficiency (that can be directly estimated from the stiffness reduction data of the laminate) to describe the interfacial degradation would be greatly advantageous. Reduction in the strength of the 0 ° ply is estimated using the S - N , curve which is typically expressed in the following form:

PREDICTION OF TENSILE F A T I G U E LIFE OF CROSS-PLY L A M I N A T E S WITH D I F F E R E N T INTERPHASES The cumulative damage scheme outlined in the previous section is used to predict the influence of an interface

S. Subramanian et al.

346

on the tensile fatigue life of cross-ply laminates. To illustrate the application of the model, the experimental results reported in ref. 20 are used.

Experimental data Subramanian et al.22 have systematically altered the fibre-matrix interface, and studied the effects on the tensile fatigue behavior of (0,903)s cross-ply laminates. A brief description of the material systems used in their study and a summary of the results is provided in this section. Three material systems, designated as 810 A, 820 A and 810 O, were used to study the effects of interphase. The same Apollo fibres and HC 9106-3 toughened epoxy matrix were used in all three material systems. However, the fibres used in the 810 A and 820 A systems received 100% and 200% industry standard surface treatment respectively, and were sized with Bisphenol-A unreacted epoxy material. The fibres in the 810 O system received 100% surface treatment and were sized with polyvinylpyrrolidone (pvp), a thermoplastic material. The amount of sizing material used in these systems was less than l wt%. The authors have verified the formation of different interphases in these material systems using a permanganic etching technique 3°. Some preliminary tensile fatigue life and damage analysis results for (0,903).~ cross-ply laminates have been reported in ref. 20. However. for completeness, the results have been reproduced here. The S - N curves for the three material systems are shown in Figure 3. The fatigue tests were performed at R = 0.1 and 10 Hz frequency• The figure indicates that the fatigue lives of cross-ply laminates with altered interphases are vastly different. Small changes in the interphase results in fatigue lives that are different by orders of magnitude. Increase in surface treatment level shifts the S - N curve to the right and increases the slope of the curve by a small amount. The use of pvp sizing material instead of Bisphenol-A epoxy shifts the S - N curve to the right and also increases the slope of the curve significantly.

Figure 4 shows the stiffness reduction curves for the three material systems at 80% load level. The figure shows that damage, as measured by stiffness reduction in the laminate, is different in these material systems. The 810 A and 820 A laminates reveal less damage, while the 810 O laminate shows significantly greater damage. The failure of the 810 A and 820 A laminates is sudden, while there is a significant increase in the stiffness reduction rate in the 810 O laminate prior to final failure. Results indicate that the damage mechanisms and failure modes in these materials are different under tensile fatigue loading. In addition to the results reported in ref. 20, the variation in the transverse crack density in these laminates was also measured as a function of cycles, and is reported in ref. 31. A master curve (independent of applied load level) of transverse crack density variation was obtained for the three material systems by multiplying the transverse crack density by (1 - ~r..... / O'static ). These normalized data were fitted with a power law curve, and are shown in Figure 5. Room temperature tensile creep test results on (90)12 laminates of the three material systems are also reported in ref. 31. These are shown in Figure O. The figure indicates that the 810 O system, with a thermoplastic sizing, exhibits the greatest creep compliance changes, and the 810 A and 820 A systems show similar creep behaviour. The data for each material system were fitted with a logarithmic curve and are shown as dashed and continuous lines in the figure. These experimental results were used to generate the inputs necessary for the fatigue life prediction model. Fatigue life prediction A schematic of the cumulative damage scheme (based on the critical element model) used to predict life of (0,903)~ cross-ply laminates is shown in Figure 7. This model could be generalized very easily for other laminates containing 0° plies. The model requires rate equations that describe damage evolution in the material as a function of cycles. These include the transverse crack density and creep compliance variation, strength degradation in the 0° ply and the

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variation of the micromechanics p a r a m e t e r defined as the efficiency of the interface, r~, as a function of cycles. The different rate equations used for the three material systems are displayed in Table 1. The power law curve representing the variation in transverse crack density as a function of cycles (Figure 5) is provided as an input into the model. The transverse crack density data are used on a one-dimensional shear lag model 32 to estimate the stiffness reduction due to matrix cracking as a function of cycles. The variation of stiffness in the 90 ° ply as a function of time due to creep (Figure 6) is also input into the model in the form of a power law equation. The total stiffness reduction in the 90 ° ply is obtained by adding the stiffness reduction due to creep and matrix cracking. The stresses in the 0 ° ply are then estimated, as a function of cycles, using the reduced properties in classical laminated plate theory.

Experimental results indicate that for a (0,903)~ cross-ply laminate, most of the stiffness reduction occurs during the first 10% of the life of the laminate. During this stage, the crack density increases in the 90 ° ply and reaches a saturation value. Transverse cracking in the 90 ° ply results in local stress redistribution in the laminate, with the 0 ° ply carrying additional load. Subsequent to the saturation of transverse matrix cracking, all the load is carried by the 0 ° ply in the laminate, and the laminate essentially behaves like a 0 ° ply. Since the laminate behaves like a 0 ° ply after the first 10% of the life, it is assumed that the life of the laminate is determined by the S - N curve of the 0 ° ply. Hence the S - N curve of the 0 ° ply is considered to represent the tensile strength reduction in the 0 ° ply of the cross-ply laminate. It must be emphasized that this assumption would not be valid if the off-axis plies carried load for a significant portion of the life. For such laminates, the residual strength reduction equation must be generalized to account for the variation in local stresses in the 0 ° ply over the entire life of the laminate. The S - N curve of the 0 ° ply is provided as input to the model. The effect of f i b r e - m a t r i x interface is included in the analysis by considering the degradation of the interracial efficiency as a function of cycles. A rate equation describing the change in interracial efficiency as a function of cycles is input into the model. The changes in tensile strength of the 0 ° ply are then estimated as a function of cycles, using the reduced interfacial efficiency in the micromechanics model. This is then used in the S - N curve of the 0 ° ply to estimate the in-situ tensile strength and life of the critical element as a function of cycles. The local stresses and in-situ tensile strength of the 0 ° ply are

S. Subramanian

348

e t al.

Table 1 Equations for the 810 A. 820 A and 810 O material system used in the fatigue damage and life prediction mudel Process modelled

810 A

810 O

Crack density vs cycles

n[1 - ((r,,,,,~ler,,,,)J = 2 (N) ......

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n = number of transverse cracks/in; N - number of cycles: t - time (s); r/ = efliciencv factor: L,,, = unidirectional transverse stiffness (msi):

E~(( ~p = unidirectional transverse stiffness including creep effects (msi - psi × 1(]": psi

then used in a m a x i m u m strain failure criterion to determine the fatigue life of the laminate. It must be pointed out here that the equations describing crack density and creep compliance variations were o b t a i n e d experimentally for these material systems, H o w e v e r , the S - N curve for the 0 ° laminate is not available for these material systems. H e n c e a logarithmic e q u a t i o n that is typical of g r a p h i t e / e p o x y unidirectional laminates is used. The same S - N curve is used for the three material systems because the same fibre and matrix were used in these materials. A n additional rate e q u a t i o n that describes the interfacial degradation as a function of cycles is used to represent the role of the interphase u n d e r fatigue loading. As m e n t i o n e d earlier, the interfacial efficiency is directly related to the longitudinal m o d u l u s of the 0 ° ply. H e n c e the rate e q u a t i o n representing the change in interracial efficiency as a function of cycles was estimated from the experimentally d e t e r m i n e d stiffness reduction curves. The stiffness reduction in the 810 A and 820 A laminates is small ( < 10%), and there is no significant stiffness reduction in these laminates after the first 10% of the life. This indicates that most of the stiffness reduction is due to d a m a g e in the 90 ° ply, and there is very little stiffness reduction in the 0 ° ply of the laminates. This idea is further confirmed by the simple ply discount t h e o r y calculations that indicate that a total of 12% stiffness reduction will occur in the laminate if the 90 ° ply is discounted completely. It must be a d d e d that, since the d y n a m i c stiffness was m e a s u r e d during fatigue tests, it is difficult to correlate the dynamic stiffness reduction with the reduction in secant m o d u l u s predicted by the shear lag model and the ply discount theory. In addition to this, the d a m a g e analysis results r e p o r t e d in ref. 20 indicate that there is very little interfacial d a m a g e in the 0 ° ply of the 810 A and 820 A laminates, while there is substantial interfacial d e b o n d i n g in the 810 O laminate. With this in mind, it is a s s u m e d that the interfacial efficiency does not vary u n d e r fatigue loading in the 810 A and 820 A laminates. H o w e v e r , the stiffness reduction data for the 810 O laminates indicate a vastly different trend. The a m o u n t of dynamic stiffness reduction is greatly in excess of the 13% reduction predicted by the simple

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ply discount theory. Also, the stiffness continues to reduce after the initial stage, and accelerates towards the end of the life of the laminate. This leads one to believe that there is significant stiffness reduction in the 0 ° ply of the laminate during fatigue loading. Since the stiffness of the 0 ° ply is directly related to the efficiency of the interface, it is claimed that there is appreciable degradation in the interfacial efficiency during tensile fatigue loading in the 810 O system. Based on the stiffness reduction data, a rate equation of the following form is used to describe the change in interfacial efficiency with cycles: 1/ = O. 76

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The equations used to represent the degradation in rt as a function of cycles for the three material systems are shown in F i g u r e 8. Using the rate equations described in T a b l e 1 (and discussed a b o v e ) , the tensile fatigue behaviour of cross-ply laminates with different interphases is predicted. The predicted values were c o m p a r e d with the experimental data reported in ref. 20.

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A comparison of the experimental and predicted fatigue lives for the three material systems at the different load levels is shown in Figures 9-11. The figures show a good correlation between experimental and predicted fatigue lives. It is also interesting to note that the micromechanics model predicts the failure mode associated with the 0 ° ply of the laminate. The model predicts an elastic failure, with no interfacial debonding, in the 810 A and 820 A laminates. In contrast, the model predicts failure accompanied by interfacial debonding in the 810 O laminates under fatigue loading at all three load levels. This agrees very well with the experimentally observed failure modes reported in ref. 20. Based on the experimental results and the predictions from the model, it is claimed that the presence of interfacial debonding influences the fatigue behaviour in the following manner. Since a simple cross-ply laminate is used in this study, the fatigue life of the laminate is determined by the failure of the 0 ° ply in the laminate. It is well known that the tensile strength of unidirectional laminates is controlled by two factors:

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LIFE (CYCLES) Figure 11 Comparisonof experimental and predicted fatigue lives of 810 O laminates the stress concentration effects near broken fibres, and the ineffective length. When the failure of the laminate is elastic, the stress concentration effects control the tensile strength. When the failure is plastic (accompanied by interfacial debonding/matrix yielding), the ineffective length controls the tensile strength of the laminate. [n general, the presence of fibre-matrix debonding reduces the stress concentration effects and increases the ineffective length. In the high-stress, low-life situation, the stress concentration effects control the failure of the 810 O laminate. The presence of debonds in the 0 ° ply alleviates the stress concentration effects in this regime and increases the fatigue life of the 810 O laminates. In the lowload, longqife regime, the ineffective length controls the final failure of the 810 O laminates. The presence of debonding increases the ineffective length and reduces the fatigue life under these conditions. This is reflected in the greater slope of the S-N curves of the 810 O laminates. It can thus be concluded that, for the material systems under investigation, the presence of fibre-matrix debonds in the 0 ° ply shifts the S-N curve to the right and also increases the slope of the S-N curve. The S-N curve of the 820 A laminate is shifted to the right, c o m p a r e d with that of the 810 A laminate. This is probably due to the lower static strength of the 820 A cross-ply laminate. The absolute stress levels at which the 820 A laminates were cycled were significantly lower than those of the 810 A laminates. The present model predicts these effects very well.

Fatigue damage prediction

m [g [email protected]@.

The stiffness reduction in the cross-ply laminates predicted using the shear lag model is used to estimate damage in the laminate as a function of cycles. D a m a g e is defined as

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Figure 10 Comparison of experimental and predicted fatigue lives of 820 ,k laminates

D(n)=

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S. Subramanian et al.

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12 Comparison of experimental and predicted damage in 810 A laminates

0.2~

In the fatigue experiments described in ref. 20, the dynamic stiffness was monitored as a function of cycles. These values are used in Equation (3) to estimate damage progression in the laminate. The experimental and predicted variation of damage in the 810 A, 820 A and 810 O laminates at different load levels is shown in Figures 12, 13 and 14 respectively. The figures indicate that the damage accumulation predicted by the model correlates well with the experimental values reported in ref. 20. It must be mentioned here that since the dynamic stiffness reduction was monitored during the fatigue experiments, and the model developed in this paper predicts the reduction in static stiffness as a function of cycles, the numerical values of experimental and predicted damage do not agree very well. But the trends predicted by the model correlate well with the experimental observations for all three material systems.

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14 Comparison of experimental and predicted damage in 810 O laminates Figure

CONCLUSIONS In this paper, a micromechanics model is used in a cumulative damage scheme to predict the tensile fatigue response of composite laminates with different fibre-matrix interfaces. The model is used to predict the influence of the fibre-matrix interface on the fatigue life and failure mode of cross-ply laminates. The role of the interphase is modelled by considering the degradation of the interfacial efficiency T/ under fatigue loading. A rate equation that describes this phenomenon is estimated from experimentally measured stiffness reduction curves. The model is used to predict the tensile fatigue behaviour of cross-ply laminates with tailored interfaces reported in ref. 20. Results indicate that the predicted fatigue life agrees well with experimental data. The fatigue lives of the 820 A laminates are higher than those of the 810 A and 810 O laminates at all three load levels. The 810 A laminates have lower life at 85% load level and higher life at 75% load level compared with the 810 O laminate• The S - N curve for the 810 O laminate has the highest slope, followed by the 820 A and 810 A laminates. The model also predicts the failure mode of the laminate under fatigue loading. The model predicts a brittle stress-concentration-controlled failure in the 810 A and 820 A laminates. In contrast, the failure in the 810 O laminates is predicted to be accompanied by interfacial debonding at all three load levels. These predictions agree very well with experimental data. This is one of the first known successful attempts to model the influence of a fibre-matrix interface on the tensile fatigue behaviour of composite laminates and to predict the experimentally observed effects of the interphase on the tensile fatigue life of laminated composites. The present model could be used to assess the possible influences of local alteration at the fibre-matrix-interface level on the long-term performance of composites. Using the proposed model, the designer can specify how the constituent materials should be put together to improve the fatigue performance characteristics of advanced composite materials.

Fatigue life of composite laminates ACKNOWLEDGEMENTS

13

The authors gratefully appreciate the support of the Air Force Phillips Laboratory, NASA Langley Research Center, The National Science Foundation Science and Technology Center DMR 9120004, and the Virginia Institute of Materials Systems.

14

REFERENCES 1

2 3 4

5 6

7 8

9

10

11 12

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