A simple laminate theory approach to the prediction of the tensile impact strength of woven hybrid composites

Simple laminate theory is used to predict the stress distribution in plain weave hybrid carbon/glass-reinforced epoxy composites under tensile loading in a direction parallel to the direction of the weave. The tensile load to cause initial failure in the carbon-reinforced plies is predicted in terms of the two-dimensional Tsai-Wu failure criterion and the measured strengths of the constituent carbon- and glass-reinforced plies. The load at final failure is predicted using the same criterion for the failure of the glass plies and assuming a reduced tensile stiffness in the carbon plies following initial failure. The theory is tested against experimental results for three woven reinforced hybrid carbon/glass composites at a quasi-static and an impact rate of strain. Reasonable agreement is obtained for the overall strength at failure, but the strain at failure is significantly overestimated.     

Microscopic fatigue damage progress in CFRP cross-ply laminates

Damage progress in toughened-type carbon fibre-reinforced plastic (CFRP) cross-ply laminates under tensile fatigue loading was measured using the replica technique. The laminate configuration was [0/90_m/0], where m = 4, 8 and 12. The damage parameters, transverse crack density and delamination ratio, were determined. A power-law model was proposed, relating the cyclic strain range and the number of cycles at transverse crack initiation. Based on experimental data, a simple shear-lag analysis combined with the modified Paris law was conducted to model the transverse crack multiplication. An extension of the shearlag analysis for laminates containing delaminations initiating from the tips of the transverse cracks was used to conduct a modified Paris law analysis for delamination growth.     

Interlaminar fatigue crack growth of cross-ply composites under thermal cycles

The fatigue growth of a fiber reinforced composite laminate was characterized under thermal cycling using a combined experimental and computational investigation. Twenty-four ply composite laminates ([0°₁₂/90°₁₂]) are fabricated with a pre-existing delamination, and subjected to thermal cycling in an environmental chamber. The large mismatch in the coefficients of thermal expansion is used to grow an interlaminar crack at the interface of the 0° and 90° laminae. This thermal fatigue crack growth behavior is investigated for different amplitudes of temperature change (ΔT = 30–140 °C). The inspection of fracture surfaces, after completion of the fatigue tests, reveals an angled or kinked crack front growth with greater propagation distances near the free-surfaces/edges. Due to the non-uniform crack growth across the specimen thickness, three-dimensional finite element analyses are performed to investigate the fatigue growth mechanisms under thermal load. From the analysis, the energy release rate as well as the mixed-mode stress intensity factors is calculated and the variations of these fracture parameters are found to be consistent with the observed crack front configuration. Using the computed results, the experimentally measured crack growth rates are also correlated with the amplitude of energy release rate, and a power law form of the fatigue law is established. The relevant coefficients as well as the threshold energy release rate are also determined. The present analysis is useful for not only understanding the fatigue delamination mechanisms under thermal cycling but also for estimating the threshold temperature variation that is needed to drive crack growth.     

A continuous damage approach to the fatigue process

The fatigue process is analyzed theoretically by studying the interaction between a macroscopic crack and continuously distributed microdamage near the crack-tips. A mode I loading case is studied, using a Dugdale crack model. The results show good agreement with Paris' law for fatigue crack propagation with an exponent approximately equal to 4. The model also predicts a finite fatigue lifetime in the sense that the crack growth rate increases without limit after a finite number of load cycles.     

碳/碳复合材料疲劳损伤失效试验研究

对单向碳/碳复合材料纵向拉-拉疲劳特性及面内剪切拉-拉疲劳特性进行了试验研究; 对三维四向编织碳/碳复合材料的纵向拉-拉疲劳特性及纤维束-基体界面剩余强度进行了试验研究。使用最小二乘法拟合得到了单向碳/碳复合材料纵向及面内剪切拉-拉疲劳加载下的剩余刚度退化模型及剩余强度退化模型, 建立了纤维束-基体界面剩余强度模型。结果显示: 单向碳/碳复合材料在87.5%应力水平的疲劳载荷下刚度退化最大只有8.8%左右, 在70.0%应力水平的疲劳载荷下, 面内剪切刚度退化最大可达30%左右; 三维四向编织碳/碳复合材料疲劳加载后强度及刚度均得到了提高; 随着疲劳循环加载数的增加, 三维四向编织碳/碳复合材料中纤维束-基体界面强度逐渐减弱。      

A continuum damage mechanics model with the strain-based approach to biaxial low cycle fatigue failure

A continuum damage mechanics model for low cycle fatigue failure of initially isotropic materials under biaxial loading conditions is presented. The expression for the equivalent strain in the fatigue damage evolution equation contains the three material parameters, and the strain intensity as well as the maximum principal strain and the volume strain for amplitudes. It is shown how these material parameters can be determined from a series of basic experiments using a cruciform specimen. Particular expressions for the equivalent strain with a smaller number of material parameters and invariants are obtained. Model predictions are found to be in satisfactory agreement with the experimental low cycle fatigue data under full ranged biaxial loadings obtained in the test using a cruciform specimen.     

The fatigue damage mechanics of a carbon fibre composite laminate: II—life prediction

The equations of fatigue damage mechanics for a carbon fibre composite laminate, developed in Part I of this paper, are applied to life prediction under constant and varying stress amplitudes. The S-N curves predicted for constant stress amplitude at various mean stresses are in good agreement with experiments. Life prediction for various block and random loadings are less satisfactory: there is an acceleration in damage growth caused by load-block interaction which is not, at present, well modelled, but can be included empirically. However, the predictions are far better than those of Miner's Rule, which is seriously non-conservative.     

A refined statistical approach to thermal fatigue life prediction

Finding new applications for ceramic materials requires a better knowledge of thermal fatigue behaviour. However, result-scattering inherent to thermal fatigue and duration of a thermal fatigue cycle lead to a lack of experimental results. For these reasons, we have developed a new approach that permits the determination of a relevant stress intensity factor exponent n with a minimum testing sample number. From knowledge of the distribution function of artificial cracks, the analytical formula of the failure probability F(N) can be completely determined. Thus, it is possible to calculate n from a correlation of F(N) with experimental results obtained for only one temperature difference. Correlations between theoretical curves F(N) and experimental results, conducted for two temperature differences, lead to the same value of n. This and the good agreement between the experimental points and the theoretical curves validate this new approach.     

A micromechanical approach for the fatigue failure prediction of unidirectional polymer matrix composites in off-axis loading including the effect of viscoelasticity

A novel micromechanical approach is used to study the fatigue failure of unidirectional polymer matrix composites subject to off-axis loading. The main advantage of the present micromechanical model lies in its ability to give closed form solutions for the effective nonlinear response of unidirectional composites and to predict the material response to any combination of shear and normal loading. The fatigue failure criterion is expressed in terms of the fatigue failure functions of the constituent materials. The micromechanical model is also used to calculate these fatigue failure functions from the knowledge of the S–N diagrams of the composite material in longitudinal, transverse, and shear loadings; thus, eliminating the need for any further experimentation. Unlike previous works, the present study accounts for the viscoelasticity of the matrix material rendering it the capability of modeling creep damage accumulation in high-temperature composite materials. The results are found to be in good agreement with the literature. In particular, for higher off-axis angles, the results are seen to be in better concurrence with the experimental data compared to when the effect of viscoelasticity is overlooked. The present approach is also capable of accounting for the strain evolution due to viscoelasticity of the matrix material.     

A micromechanistic-based approach to fatigue life modeling of titanium-matrix composites

Fatigue life modeling of titanium-based metal-matrix composites (MMCs) was accomplished by combining a unified viscoplastic theory, a non-linear micromechanics analysis and a damage accumulation model. The micromechanics analysis employed the Bodner-Partom unified viscoplastic theory with directional hardening. This analysis was then combined with a life-fraction fatigue model to account for the time-dependent component of fatigue damage. The life-fraction fatigue model involved the linear summation of damage from the fiber and matrix constituents of the composite. A single set of empirical constants for the life-fraction fatigue model were established for each of two titanium MMCs reinforced with silicon carbide fibers: SCS-6/Ti-15-3 and SCS-6/ TIMETAL®21s. The predicted fatigue lives were within one order of magnitude of the experimental data for different loading conditions: isothermal fatigue, and both in-phase and out-of-phase thermomechanical fatigue. MMCs modeled included cross-ply, quasi-isotropic and unidirectional SCS-6/TIMETAL®21s, and cross-ply and quasi-isotropic SCS-6/Ti-15-3 laminates.     

Thermodynamic analysis of fatigue failure in a composite laminate

We put forward a thermodynamic approach for analyzing fatigue failure in a composite laminate. We show that fatigue is an irreversible progression of increasing entropy that accumulates until it reaches a critical value called the fracture fatigue entropy (FFE) at the onset of failure. Extensive series of fatigue tests are carried out that involve load-controlled tension-tension, and displacement controlled fully-reversed bending fatigue with three different stress ratios as well as constant- and variable-loading. The role of hysteresis energy in the entropy generation is investigated. FFE values are calculated based the experimental data obtained for temperature and hysteresis energy of a woven Glass/Epoxy (G10/FR4) laminate. The concept of tallying entropy accumulation and the use of FFE are useful for determining the fatigue life of composite laminates undergoing cyclic loading.     

Shear mechanism modelling of heavy tow braided composites using a meso-mechanical damage model

Heavy tow braid reinforced composites are a potential substitute for metals in automotive and other transport applications. These composites, if properly designed, can provide lightweight efficient load bearing structural members that can also absorb high specific energy under impact and crash loading. Many of these components are ‘beam like’ members that must resist large transverse deformations at high force levels, thereby absorbing high levels of energy. This class of composite component is particularly considered in this paper.An effective means to achieve high energy absorption is careful design of the fabric architecture so that shearing mechanisms of the fibre/matrix interface, without premature fibre failure, are possible. Characterisation and modelling of progressive shear damage and failure occurring in biaxial carbon and glass braided composites are investigated. Fibre re-orientation and fibre/matrix interface damage is measured using an optical strain measuring method based on digital image correlation (DIC). This is then used to provide input to a meso-mechanical damage model in an explicit finite element code. A modelling approach using coupled layers of equivalent unidirectional plies is used to represent the biaxial braid composite and validation of the approach has been performed against test coupons and beam structures loaded transversally to failure.     

A unified approach to damage accumulation and fatigue crack growth

An approach is proposed to the theory of fatigue cracks propagation based on the following postulate: a growing crack at least once in a cycle becomes a nonequilibrium one (in the Griffith's sense) under the condition that the resistance to crack growth is calculated with an account of damage accumulated at the crack tip during the loading history. The theory is used for nonuniaxial stress states including jumplike growth, stops, kinking and branching phenomena. The general structure of differential equations is discussed for the averaged crack growth rate under nonuniaxial loading.     

A model of continuum damage mechanics for fatigue failure

This paper describes the development of a generalized model of continuum damage mechanics for fatigue fracture. With the introduction of a new damage effect tensor, the necessary constitutive equations of elasticity and plasticity coupled with damage are for the first instance derived. This is followed by the formulations of fatigue damage dissipative potential function and a fatigue damage criterion which are required for the development of a fatigue damage evolution equation. The fatigue evolution model is based on the hypothesis that the overall fatigue damage is induced by the summation of elastic and plastic damages.The validity of the damage model proposed is verified by comparing the predicted and measured number of cycles to failure for ten tensile specimens each applied with different load ranges and excellent agreement has been achieved.University of Science and Technology of China     

Application of continuum damage mechanics to vibration fatigue life prediction

It is pivotal to predict the multiaxial vibration fatigue life during mechanical structural dynamics design. An algorithm of the finite element method implementation for multiaxial high cycle fatigue life evaluation is proposed, on the basis of elastic evolution model of continuum damage mechanics. By considering structural dynamic characteristics, namely, resonant frequencies and mode shapes, this algorithm includes a modal analysis and harmonic analysis, which makes this different from existing fatigue life prediction methods. A 10% decrease in the resonant frequency is regarded as the failure criterion. A critical damage value was obtained, which indicates mesocrack initiation fulfilment. To validate the effectiveness of the algorithm, auto‐phase sine resonance track‐and‐dwell experiments were conducted on notched cantilever beams made of Ti‐6Al‐4V alloy. The life predictions are conservative and in good agreements with the experimental results, which are mainly distributed within a scatter band of 2. This investigation could provide technical support for structural dynamics design and the analysis of reusable spacecraft.     

A micro-mechanics damage approach for fatigue of composite materials

A new model for fatigue damage evolution of polymer matrix composites (PMC) is presented. The model is based on a combination of an orthotropic damage model and an isotropic fatigue evolution model. The orthotropic damage model is used to predict the orthotropic damage evolution within a single cycle. The isotropic fatigue model is used to predict the magnitude of fatigue damage accumulated as a function of the number of cycles. This approach facilitates the determination of model parameters since the orthotropic damage model parameters can be determined from available data from quasi-static-loading tests. Then, limited amount of fatigue data is needed to adjust the fatigue evolution model. The combination of these two models provides a compromise between efficiency and accuracy. Decomposition of the state variables down to the constituent scale is accomplished by micro-mechanics. Phenomenological damage evolution models are then postulated for each constituent and for the micro-structural interaction among them. Model parameters are determined from available experimental data. Comparison between model predictions and additional experimental data is presented.     

A micromechanical approach for the prediction of the time-dependent failure of high temperature polymer matrix composites

In the present study, a novel micromechanical approach is introduced to study the time-dependent failure of unidirectional polymer matrix composites. The main advantage of the present micromechanical model lies in its ability to give closed-form solutions for the effective nonlinear response of unidirectional composites and to predict the material response to any combination of shear and normal loading. The creep failure criterion is expressed in terms of the creep failure functions of the viscoelastic matrix material. The micromechanical model is also used to calculate these creep failure functions from the knowledge of the creep behavior of the composite material in only transverse and shear loadings, thus eliminating the need for any further experimentation. The composite material used in this study is T300/934, which is suitable for service at high temperatures in aerospace applications. The use of micromechanics can give a more accurate insight into the failure mechanisms of the composite materials in particular at high temperatures where the general behavior of the polymer matrix composite is governed by matrix viscoelasticity and the time-dependent failure of the matrix is a localized phenomenon. The obtained creep failure stresses are found to be in reasonable agreement with the experimental data.     

Microscopic-damage-based criterion for fatigue failure prediction

A computer-aided X-ray rocking curve analyser was developed to monitor the accrued microstructural damage occurring during low cycle fatigue of an aluminium alloy. These results indicated a linear relationship between the X-ray rocking curve half-width and the fraction of life. The resultant damage-assessment curve provided a nondestructive means of estimating the time to failure in a sample with unknown prior loading history. This failure criterion was found to be independent of the strain amplitude and was equally applicable to either high cycle or low cycle fatigue.     

An approach to fatigue life modeling in titanium-matrix composites

A review of the procedures developed by the author and his colleagues over the last several years for predicting elevated-temperature fatigue life of metal-matrix composites is presented. Modeling approaches involve concepts of both linear and non-linear summation of damage from cycle-dependent as well as time-dependent mechanisms. The analyses, further, treat the micromechanical stresses in the constituents as parameters in the life prediction models. The material characterized is SCS-6/Timetal®21S, a metastable beta titanium alloy reinforced with continuous SiC fibers. Modeling is applied to isothermal fatigue at different frequencies and temperatures, and thermomechanical fatigue (TMF) under both in-phase and out-of-phase loading conditions at different temperature ranges and maximum temperatures. Experimental data are used as the basis for determining the parameters embedded in the models. The numerical results, in turn, provide insight into the dominant mechanisms controlling fatigue life under a given condition. The capability to correlate experimental data from a wide variety of test conditions for several versions of a damage summation model is demonstrated.     

一种基于复合材料剩余强度的衍生疲劳损伤模型

为了研究纤维增强树脂复合材料在疲劳载荷作用下的损伤发展规律,提出了一种基于复合材料剩余强度的归一化衍生疲劳损伤模型。在该模型中,假定累积损伤与应力水平呈线性关系,可以由拉-拉疲劳试验的应力水平的损伤曲线衍生出未试验的应力水平的损伤曲线。对直径为8 mm的碳纤维增强树脂复合材料(CFRP)索材进行了不同应力幅的疲劳试验,并同时采用了文献中玻璃纤维增强树脂复合材料(GFRP)层合板的试验数据验证模型的可靠性,试验结果表明:损伤模型能较好地反映出三阶段的发展规律,衍生的损伤曲线与试验数据拟合出来的损伤曲线偏离度较小。此外,本文还研究了应力水平对复合材料损伤演化的影响,结果表明随着应力水平的增大,损伤曲线相邻阶段的边界变得不明显。