Recent developments on damage modeling and finite element analysis for composite laminates: A review

Under complex environments such as continuous or cyclic loads, the stiffness degradation for the laminated composites such as the carbon fiber reinforced polymer matrix composites is an important physical and mechanical response to the damage and failure evolution. It is essential to simulate the initial and subsequent evolution process of this kind of damage phenomenon accurately in order to explore the mechanical properties of composite laminates. This paper gives a comprehensive review on the general methodologies on the damage constitutive modeling by continuum damage mechanics (CDM), the various failure criteria, the damage evolution law simulating the stiffness degradation, and the finite element implementation of progressive failure analysis in terms of the mechanical response for the variable-stiffness composite laminates arising from the continuous failure. The damage constitutive modeling is discussed by describing the evolvement of damage tensors and conjugate forces in the CDM theory. The failure criteria which interpret the failure modes and their interaction are compared and some advanced methods such as the cohesive theory which are used to predict the damage evolution properties of composites are also discussed. In addition, the solution algorithm using finite element analysis which implements progressive failure analysis is summarized and several applicable methods which deal with the numerical convergence problem due to singular finite element stiffness matrices are also compared in order to explore the whole failure process and ultimate load-bearing ability of composite laminates. Finally, the multiscale progressive failure analysis as a popular topic which associates the macroscopic with microscopic damage and failure mechanisms is discussed and the extended finite element method as a new finite element technique is expected to accelerate its practical application to the progressive failure analysis of composite laminates.     

基于径向基函数神经网络的CFRP切削力预测

碳纤维增强树脂基复合材料(CFRP)加工中基体相极易因切削力过大而破坏,并迅速扩展至加工表面以下而形成损伤。为了准确预测其切削力并加以控制,基于实验切削力数据建立了人工神经网络切削力模型,预测了不同纤维角度、切削深度和刀具角度下加工CFRP的切削力变化规律,并完成了不同刀具角度及切削参数下典型纤维角度CFRP单向板的直角切削实验,对预测模型进行验证,其预测精度可达85%以上。结合成屑过程在线显微观测结果可知:纤维角度是影响CFRP切削力的主要因素, 0°~135°范围内,切屑形成方式为切断型和开裂后弯断型;切削力随纤维角度增大呈先减小后增大的趋势, 135°时最大,随切削深度增加,切削力总体呈增大趋势。      

Machining of UD-GFRP composites chip formation mechanism

The chip formation mechanism in orthogonal machining of unidirectional glass fiber reinforced polymer (UD-GFRP) composites is simulated using quasi-static analysis. Dynamic explicit finite element method with mass scaling is used for analysis to speed up the solution. A two-dimensional, two-phase micromechanical model with elastic fiber, elasto-plastic matrix and a cohesive zone is used to simulate the debonding interface between the fiber and the matrix. The elements of the fiber are failed once the maximum principal stress reaches the tensile strength and the matrix elastic modulus is degraded once the ultimate strength is reached. The effect of fiber orientation, tool parameters and operating conditions on fiber and matrix failure and chip size is also investigated. The degradation of the matrix adjacent to the fiber occurs first, followed by failure of the fiber at its rear side. The extent of sub-surface damage due to matrix cracking and interfacial debonding is also determined.     

Micro-mechanical modeling of machining of FRP composites – Cutting force analysis

Orthogonal machining of unidirectional carbon fiber reinforced polymer (UD-CFRP) and glass fiber reinforced polymer (UD-GFRP) composites is simulated using finite element method (FEM). A two-phase micro-mechanical model with fiber assumed elastic and the matrix elasto-plastic is used to estimate the cutting forces during machining. A cohesive zone simulated the interface debonding between the fiber and matrix. Fiber failure was based on maximum principal stresses reaching the tensile strength. The matrix elastic modulus was degraded to include damage once yield strength was reached. The model assumes plane strain and quasi-static condition. The cutting forces during orthogonal machining were studied both experimentally and numerically for a range of fiber orientations (θ), depths of cut (t) and tool rake angles (γ). The contact forces developed between the tool and the fiber provided a good estimate of the cutting (F_h) and thrust (F_v) forces during the orthogonal cutting process. The failure of fiber is found to be a combination of crushing and bending, with the bending effect becoming more significant as the fiber orientation changes from 90° to 15°.     

Failure prediction for a glass/epoxy cruciform specimen under static biaxial loading

Material models were developed to predict the mechanical behavior of glass/epoxy multidirectional laminates under complex stress states. An incremental plane stress analysis was performed, taking into account the anisotropic material non-linearity, separate damage onset conditions and distinct post-failure stiffness degradation rules. Theoretical formulations were implemented in a shell element of the 1st order shear deformation theory. Numerical results were validated via comparison with test data from cruciform specimens subjected to static biaxial tensile loading. Local strain gauge and full-field strain measurements, obtained using the Digital Image Correlation (DIC) technique, corroborated numerical predictions. Improved strength and failure mode results were derived when, in addition to stiffness reduction, compressive strength degradation in the fiber direction was also considered.     

复合材料层合板多尺度交互渐进损伤分析

纤维增强复合材料强度的准确表征是复合材料力学性能研究的核心问题之一。该文以碳纤维增强树脂基复合材料层合板为研究对象,基于宏观-细观多尺度分析方法,根据复合材料的物理失效模式分别给出了基体和纤维的细观失效准则,同时考虑基体失效对复合材料层合板纤维轴向力学性能的影响。提出了新的刚度退化方式,可准确表征复合材料层合板的损伤演化过程,开展了复合材料层合板四点弯模型的多尺度交互渐进损伤分析和试验验证。结果表明:基于多尺度方法的复合材料层合板宏-细观交互渐进损伤分析结果与试验结果吻合较好,新的刚度退化方式可以准确模拟层合板的失效过程。     

A discrete element method for the simulation of CFRP cutting

Orthogonal machining of unidirectional carbon fiber-reinforced polymer (UD-CFRP) composites is simulated using discrete element method (DEM). The objective of this work is to present a simple numerical model that allows the study the machining of unidirectional composites during orthogonal cutting. To control the physicochemical phenomena that occur during cutting, it is necessary to identify the parameters of contact, very difficult to measure experimentally. The DEM numerical simulation is presented then as an alternative to the problem. This tool has helped to recreate the physical mechanisms identified experimentally and to understand the origin of the abrasive wear of carbide tools. The observation of the chip formation using a high speed video camera made possible to validate qualitatively the results of numerical simulation by discrete elements. This tool can also determine the cutting forces quite close to reality.     

Investigating the effect of machining processes on the mechanical behavior of composite plates with circular holes

The influence of the machining quality on the mechanical behavior of CFRP composites is yet not fully understood. There are only few works in the literature that have investigated the effect of the machining quality on CFRP. In fact, most of these works focus only on conventional machining such as axial or orbital drilling. The aim of this paper is to examine the influence of two machining processes namely conventional machining (CM) and abrasive water jet machining (AWJM) on the mechanical behavior of composite plates under cyclic loading. For this purpose, an experimental study using several composite plates drilled with a cutting tool and an abrasive water jet machining was carried out. In order to study the impact of the process of machining on the mechanical behavior, thermographic infrared testing and fatigue cyclic tests were performed to assess temperature evolutions, stiffness degradation, and the damage evolution in these plates. Fatigue testing results have shown that the damage accumulation in specimens drilled with CM process was higher than the AWJM specimens. Furthermore, the endurance limit for a composite plate drilled with CM was approximately 10% inferior compared to specimens drilled with AWJM. This difference can be related to the initial surface integrity after machining induced by the difference in the mechanism of material’s removal between the two processes used.     

An analytical method for predicting cutting forces in orthogonal machining of unidirectional composites

Since the chip-formation mechanism in orthogonal machining of composites is different from that of metals, the cutting theories developed for metals cannot be directly used for orthogonal machining of composites. The objective of this research was to develop a new analytical method using energy method to predict the machining forces for orthogonal machining of unidirectional polymer–matrix composites (PMCs) for fiber orientations ranging from 90° to 180° Experiments were conducted to verify the validity of the proposed model using tools with rake angles of 5°, 10°, 15°, and 20°.     

Analysis of Chip Removal Operations via New Quick-Stop Device

Machining is obviously indispensable to industrial manufacture, a process whereby a workpiece takes its planned shape after proper chip removal. The type and the size of a chip from such a process are determined by a set of factors, the analysis of which can provide valuable insights into the cutting process. In this study, a new quick-stop device (QSD) for chip removal was designed, manufactured, and employed in an analysis of chip formation in chip removal with cutting tool at varying cutting speeds. The samples competently illustrate the differences in the formation of chips at various cutting speeds. Depending on material and cutting conditions, a chip may be continuous or discontinuous. Employing metallographic techniques, the present study analyzed the orthogonal cutting of aluminum 5000 with cutting tool. During the experiments, the built-up edges (BUEs), the surface quality, and the interactions among machining parameters were observed. At the end, a frozen chip with a BUE was divided into seven sections. The results show that the new QSD is effective and BUEs have a direct effect on the quality of a workpiece's surface and additionally can increase the penetration depth and machining forces.     

三维复合材料层合板渐进损伤非线性分析模型

为有效反映复合材料层合板层间相互作用和材料损伤非线性,建立了中等尺度的三维复合材料层合板渐进损伤分析模型。非线性渐进损伤分析过程包括应力求解、材料损伤失效判据及材料性能退化方案3个方面。讨论了损伤材料性能退化方案,引入与材料损伤模式相对应的损伤变量表征材料点的损伤状态,材料的刚度矩阵按损伤变量退化。基于该模型可成功预测复合材料层合板损伤起始、扩展直至最终失效的整个过程和极限强度。经文献试验数据验证,12种不同铺层顺序层合板的计算强度与试验数据均吻合较好,表明该模型在复合材料层合板极限强度预测上的有效性。     

A phenomenologically based damage model for textile composites with crimped reinforcement

A phenomenological damage model for textile composites with woven or braided reinforcement is presented and verified in this paper. Essential mechanical questions are clarified with regard to the dominant damage mechanisms and the definition of representative equivalent layers. Using the framework of continuum damage mechanics, damage is defined as the change of the tensor of elasticity. The initiation of damage is described using novel failure criteria based on the Failure-Mode-Concept. Damage variables and associated evolution laws are introduced to describe the subsequent degradation of the material stiffness. The capability of the proposed model is shown for woven thermoplastic composites made of hybrid glass–polypropylene yarns.     

Low velocity impact modeling in composite laminates capturing permanent indentation

This paper deals with impact damage and permanent indentation modeling. A numerical model has been elaborated in order to simulate the different impact damage types developing during low velocity/low energy impact. The three current damage types: matrix cracking, fiber failure and delamination, are simulated. Inter-laminar damage, i.e. interface delamination, is conventionally simulated using interface elements based on fracture mechanics. Intra-laminar damage, i.e. matrix cracks, is simulated using interface elements based on failure criterion. Fiber failure is simulated using degradation in the volume elements. The originality of this model is to simulate permanent indentation after impact with a “plastic-like” model introduced in the matrix cracking elements. This model type is based on experimental observations showing matrix cracking debris which block crack closure. Lastly, experimental validation is performed, which demonstrates the model’s satisfactory relevance in simulating impact damage. This acceptable match between experiment and modeling confirms the interest of the novel approach proposed in this paper to describe the physics behind permanent indentation.     

Study of trimming damages of CFRP structures in function of the machining processes and their impact on the mechanical behavior

The main focus of this paper is to investigate the defects generated by different machining processes (namely burr tool machining, abrasive water jet machining ‘AWJM’ and abrasive diamond cutter ‘ADS’) and their impact on the mechanical behavior of CFRP in quasi-static (compression and inter-laminar shear) and tensile–tensile fatigue tests. The cutting conditions are selected so that different levels of degradation can be obtained. The machined surface is characterized using roughness measuring devices with and without contact and SEM observations. The results show that the defects generated during the trimming process with a cutting tool are fibers pull-out and resin degradation. These defects are mainly located in the layers with the fibers oriented at −45° and 90°. However, when using abrasive water jet and abrasive diamond processes, the defects generated have the form of streaks and are not dependent on the fiber orientation. Furthermore, the results of quasi-static tests performed on specimens machined by cutting tools show that AWJ specimens offer a better resistance in compression but the ADS samples offer higher inter-laminar-shear strengths. Moreover, the results of fatigue tests show that specimens machined with a burr tool offer higher endurance limit. Finally, it is concluded that the type and the mode of the mechanical loading (quasi-static fatigue) affect the mechanical response of CFRP and favor a given machining process.     

Frequency analysis and characterization in orthogonal cutting of glass fiber reinforced composites

This study discusses frequency analysis based on frequency spectrum and autoregressive (AR) time series model, and process characterization in orthogonal cutting of fiber–matrix composite materials. A sparsely distributed idealized composite material, namely a glass fiber reinforced polyester (GFRP) was used as the workpiece. The analysis method employs a force sensor and the signals from the sensor are processed using either the fast Fourier transform (FFT) technique or AR time series model. Signal distortion measure based on discrimination information is also introduced. The experimental correlations between the different chip formation mechanisms and power spectrum or AR model coefficients are then established. In particular, only those features that are most sensitive to different types of cutting mechanisms are selected by feature extraction method in AR modeling. Selected features are used to characterize the chip formation. Discrimination information measure proves to be useful in signal analysis when any characteristic of the cutting process is apparent in the form of spectral peaks. Effects of fiber orientation, cutting parameters and tool geometry on the cutting mechanisms and surface quality are also discussed.     

Machining and surface integrity of fibre-reinforced plastic composites

The current focus of manufacturing research on fibre-reinforced plastics (FRP) is composed of the search for efficient processing techniques capable of providing high quality machined surfaces. Very limited work has been performed to identify the influence of manufacturing processes like edge-trimming and drilling on material performance. Recent reports suggest that process-induced damage may affect the mechanical behaviour of FRP materials. Therefore an experimental study of orthogonal cutting was conducted on the edge trimming of unidirectional and multi-directional graphite/epoxy composites with polycrystalline diamond tools. The effects of tool geometry and operating conditions were evaluated from an analysis of chip formation, cutting force, and machined surface topography. All aspects of material removal were found to be primarily dependent on fibre orientation. Discontinuous chip formation was noted throughout this study, regardless of machining parameters. Three distinct mechanisms in the edge trimming of fibre-reinforced composite material including a combination of cutting, shearing, and fracture along the fibre/matrix interface were observed. An investigation conducted on the compression, flexural and impact strength of graphite/epoxy composites machined by both traditional and non-traditional techniques, confirms that manufacturing characteristics may not only affect bulk properties but also influence the initiation and propagation of failure.     

Predicting evolution of ply cracks in composite laminates subjected to biaxial loading

An energy-based model is developed to predict the evolution of sub-critical matrix crack density in symmetric multidirectional composite laminates for the case of multiaxial loading. A finite element-based numerical scheme is also developed to evaluate the critical strain energy release rate, G_Ic, associated with matrix micro-cracking, a parameter that previously required fitting with experimental data. Furthermore, the prediction scheme is improved to account for the statistical variation of G_Ic within the material volume by using a two-parameter Weibull distribution. The variation of G_Ic with increasing crack density is also accounted for based on reported experimental evidence. The simulated results for carbon/epoxy and glass/epoxy cross-ply laminates demonstrate the ability of the improved model to predict the evolution of multidirectional ply cracking. By integrating this damage evolution model with the synergistic damage mechanics approach for stiffness degradation, the stress-strain response of the studied laminates is predicted. Finally, biaxial stress envelopes for ply crack initiation and pre-determined stiffness degradation levels are predicted to serve as representative examples of stiffness-based design and failure criterion.     

A progressive damage simulation algorithm for GFRP composites under cyclic loading. Part II: FE implementation and model validation

The FE implementation of FADAS, a material constitutive model capable of simulating the mechanical behaviour of GFRP composites under variable amplitude multiaxial cyclic loading, was presented. The discretization of the problem domain by means of FE is necessary for predicting the damage progression in real structures, as failure initiates at the vicinity of a stress concentrator, causing stress redistribution and the gradual spread of damage until the global failure of the structure. The implementation of the stiffness and strength degradation models in the principal material directions of the unidirectional ply was thoroughly discussed. Details were also presented on the FE models developed, the computational effort needed and the definition of final failure considered. Numerical predictions were corroborated satisfactorily by experimental data from constant amplitude uniaxial fatigue of multidirectional glass/epoxy laminates under various stress ratios. The validation of predictions included fatigue strength, stiffness degradation and residual static strength after cyclic loading.