Numerical simulation of delamination in laminated composite components – A combination of a strength criterion and fracture mechanics

An approach for the numerical treatment of delamination in laminated composite components is presented. A first ply failure criterion is employed to predict delamination initiation, while delamination propagation is analyzed using linear elastic fracture mechanics. The combination of initiation and propagation criteria yields a conservative estimation of the load earring capacity of a structure. Furthermore, the growth stability, the sensitivity of the results with respect to a change in the interface properties, and the non-linear structural response caused by the delamination growth process are determined. Two structures are investigated, which show the capability of the proposed approach, a curved laminate and a double lap shear test specimen.     

INTERLAMINAR SHEAR STRESS ANALYSIS OF COMPOSITE LAMINATE WITH LAYER REDUCTION TECHNIQUE

Interlaminar stress plays an important role in the delamination failure of laminated composites. A recently presented theory, the Interlaminar Shear Stress Continuity Theory (ISSCT), can directly and accurately predict interlaminar shear stresses in laminated composites by the constitutive equations. The present study further generalizes the derivation to a complete form from which many displacement-based laminate theories can be derived. Most of all, both the single-layer and multiple-layer approaches are incorporated into the analysis in the thickness direction. The laminate is discretized into several sublaminates and, then, a layerwise theory is applied in the analysis of this reduced laminate. This reduction in the number of layers used in the analysis makes the calculation of interlaminar shear stresses on the interested interface in a thick laminate more efficient. In addition, numerical solutions in closed-form and finite element form for laminates under cylindrical bending and bidirectional bending are examined. It is found that in the thickness direction the cubic order of the interpolation function and the discretization with four to six sublaminates can reduce the computational efforts dramatically and retain the accuracy of the predicted stresses within ±8 per cent.     

Failure analysis of a hybrid composite structural beam

The purpose of this study was to identify the failure mode of a particular composite structural beam developed for the civil infrastructure market and to develop a strength prediction that could be utilized in fatigue life predictions. First, a global–local finite element stress analysis is utilized to examine the possibility of compression failure. We then investigate the possibility of a delamination failure using a successive sub-modeling approach that allows detailed analysis of the inter-laminar stresses in regions of high stress gradients, including free edges and tapered laminates. The results of the analyses are compared with experimental test data from full-scale bending tests. The results indicate a compression dominated failure in the top flange in the vicinity of the load patch. This study highlights the difficulty in applying a stress-based approach to predicting delamination failure, particularly in complex laminated structures.     

低速冲击作用下碳纤维复合材料铺层板的损伤分析

建立了一个有效计算模型, 以分析碳纤维复合材料层合板在低速冲击作用下的层内和层间失效行为。针对铺层板的层内损伤, 在基于应变描述的Hashin 失效准则的基础上, 建立了单层板的逐渐累积损伤分析模型;针对铺层板的脱层损伤, 建立了各向同性脱层损伤模型, 通过结合传统的应力失效准则和断裂力学中的能量释放率准则定义了界面损伤演化规律, 并在潜在产生脱层的区域模拟为粘结接触, 并将脱层损伤模型作为界面的接触行为。该计算模型通过商用有限元软件ABAQUS/ Explicit 的用户子程序实现。使用该计算模型对碳纤维增强环氧树脂复合材料层合板在横向低速冲击作用下的损伤和变形行为进行预测分析。数值仿真的结果与试验结果进行了比较, 取得了满意的结果, 验证了该模型的正确性。      

Dynamic behavior of delaminated plates considering progressive failure process

The paper is to study on dynamic response behavior of the delaminated composite plates considering progressive failure process. A formula of element stiffness and mass matrices for the composite laminates is deduced by using the first-order shear deformation theory combined with the selecting numerical integration scheme. A damping model is constituted by a generalized orthogonal damping model on basis of Adams' strain energy method. A virtual interface linear spring element is also employing for avoiding the overlap and penetration phenomenon between the upper and lower sublaminates at the delamination region. The failure analysis method for the delaminated plates under dynamic loading is established by a modified Newmark direct integral method in conjunction with Tsai's failure criterion and corresponding stiffness degradation scheme. By some numerical examples, the effects of frequency of dynamic load, delamination length and location, and reduction of structure stiffness during the progressive failure process upon dynamic behavior of the delaminated composite plates are discussed. The method and conclusions would be useful for composite structures designers.     

复合材料层合板低速冲击损伤的有限元模拟

建立了用于预测复合材料层合板在低速冲击作用下损伤的3D有限元模型。采用应变描述的失效判据来判断铺层层内的各类损伤, 如纤维断裂、 纤维挤压、 基体开裂、 基体挤裂, 并结合相应的刚度折减方案对失效单元进行刚度折减。使用界面元模拟层间区域, 结合传统的应力失效判据和断裂力学中的能量释放率准则来定义分层损伤的起始和演化规律, 提出了一种界面元损伤起始强度沿厚度方向的分布函数。通过对数值仿真结果和实验结果的比较, 验证了模型的合理性和准确性。      

A theoretical approach for the assessment of intralaminar fracture mode and toughness of multilayered composites

Analytical evaluation of fracture toughness of a multilayered composite laminate was well-established using modified crack closure integral (MCCI) approach based on test data on the failure load. For this purpose the crack initiation direction, which is treated as a branch crack direction for the theoretical prediction, is required. The crack initiation direction in a multilayered composite laminate depends on mode of failure. In the present work, a fracture parameter n ^* is introduced to predict the mode of failure in multilayered composite having a crack and is validated. Analytical relationship for the prediction of fracture toughness of multilayered composite between a base laminate and its constituent sublaminates is also arrived at. With available test data on the toughness of a set of sub-laminates, toughness of base laminate is determined and validated. The present approach is useful in evaluating the load carrying capability of composite structures with defects in the form of cracks and this information is valuable for design.     

Failure load prediction of laminates repaired with a scarf-bonded patch using the damage zone method

The damage zone method (DZM) is an efficient way to predict the failure of composite structures with a minimum of real testing. Particularly, it is useful when the failure mechanism is too complicated to be accurately analyzed by a merely numerical method. The aim of this study was to use the damage zone model to predict the failure load of repaired laminates, in which scarf-bonded joints were used for repair. The model uses a test-based critical damage zone and stress-based failure criteria. A total of 45 carbon-epoxy composite (USN) laminate scarf-repaired specimens were first tested with two different defect sizes, four scarf angles, and three overlap layer sizes. The Tsai-Wu and Tsai-Hill criteria were used for the laminate, and the maximum shear stress criterion for the adhesive was adopted to predict failure onset. The predicted failure loads were compared to test results and a good agreement was obtained with a 9.2% maximum deviation for almost all parameters with the exception of a case with an unrealistically large scarf angle. To verify the feasibility of the DZM for different material, additional 30 repair specimens using other unidirectional carbon-epoxy laminate were then also tested and the predictions were confirmed by the results of the experiment.     

各向异性复合材料开孔板拉伸强度预测及模型验证

基于有限断裂力学方法建立了一种预测多向复合材料开孔板拉伸强度的通用和半经验模型。该模型同时采用基于应力形式的失效准则和基于能量形式的失效准则预测失效。模型仅需铺层弹性常数、无缺口层合板的强度以及0°铺层的断裂韧性等参数。基于线弹性断裂力学建立了多向复合材料层合板的断裂韧性与0°铺层断裂韧性之间的关系, 进而预测了任意铺层复合材料开孔板发生纤维主导拉伸失效时的强度。将模型预测结果与开孔板拉伸强度的试验数据进行了对比验证, 预测误差最大为9.7%, 与点应力和平均应力等方法的对比表明, 该模型的预测精度高于传统的特征长度方法。      

Progressive Failure Modeling in Notched Cross-Ply Fibrous Composites

This study models and simulates progressive failure initiating from a notch tip of a laminated fibrous composite specimen subjected to tensile in-plane loading. The micro/macro-level approach is used. The micro-level analysis uses the 3-D unit-cell model while macro-level analysis uses the finite element analysis technique. A cross-ply laminate with double-edge notches was studied to investigate delamination, fiber splitting, and transverse matrix cracking in the specimen. Numerical results are compared to previous experimental work.     

Compressive behaviour of thin-skin stiffened composite panels with a stress raiser

The in-plane compressive behaviour of thin-skin stiffened composite panels with a stress concentrator in the form of an open hole or low velocity impact damage is examined analytically. Drop weight impact in laminated polymer composites causes matrix cracking, delaminations and fibre breakage, which together can seriously degrade the laminate compressive strength. Experimental studies, using ultrasonic C-scan images and X-ray shadow radiography, indicated that the overall damage resembles a hole. Under uniaxial compression loading, 0° fibre microbuckling surrounded by delamination grows laterally (like a crack) from the impact site as the applied load is increased. These local buckled regions continued to propagate, first in discrete increments and then rapidly at failure load. The damage pattern is very similar to that observed in laminated plates with open holes loaded in compression. Because of this resemblance, a fracture mechanics model, developed initially to predict notched compressive strength, was applied to estimate the compression-after-impact (CAI) strength of a stiffened panel; in the analysis the impact damage is replaced with an equivalent open hole. Also, the maximum stress failure criterion is employed to estimate the residual compressive strength of the panel. The unnotched compressive strength of the composite laminate required in the analysis is obtained from a three-dimensional stability theory of deformable bodies. The influence of the stiffener on the compressive strength of the thin-skin panel is examined and included in the analysis. A good agreement between experimental measurements and predicted values for the critical failure load is obtained.     

Stress intensity factor for a three-layered plate with a crack in the center layer

The objective of this study is to model the laminated composite as a multilayered plate each layer being made of a different material. With a crack in the mid-layer of the laminate, the stresses can vary in all three space coordinate directions and the problem is recognized as a three-dimensional one. A laminate plate theory is developed by application of the minimum complementary energy theorem in variational calculus such that the qualitative three-dimensional character of the crack edge stresses is retained while approximations are made in a quantitative sense on the stress intensity factor.Numerical values of the stress intensity factors for different construction of the laminate are reported and compared with the same size plate made of a single homogeneous material. When the modulus of elasticity of the middle layer which contains the crack is lower than that of the outer layers, the load transmission to the crack site as measured by the stress intensity factor can be reduced significantly. The present model assumes failure by crack propagation in only one layer of the laminate. Other possible modes of failure such as cohesive and/or adhesive fracture in laminated structures have yet to be explored.     

Composite laminate failure analysis using multicontinuum theory

Damage in a composite material typically begins at the constituent level and may, in fact, be limited to only one constituent in some situations. An accurate prediction of constituent damage at sampling points throughout a laminate provides a genesis for progressively analyzing failure of a composite structure from start to finish. Multicontinuum Theory is a micromechanics based theory and associated numerical algorithm for extracting, virtually without a time penalty, the stress and strain fields for a composites’ constituents during a routine finite element analysis. A constituent stress-based failure criterion is used to construct a nonlinear progressive failure algorithm for investigating the material failure strengths of composite laminates. The proposed failure analysis methodology was used to simulate the nonlinear laminate behavior and progressive damage of selected laminates under both uniaxial and biaxial load conditions up to their ultimate strength. This effort was part of a broader project to compare the predictive capability of current composite failure criteria.     

复合材料层合板缺口强度的CDM三维数值模型

针对复合材料层合结构缺口强度问题,基于连续损伤力学（CDM）提出了一种三维损伤数值模型。模型区分了层内损伤（纤维失效、纤维间失效）和层间分层损伤的不同失效模式。采用三维Puck准则与Aymerich准则对上述2类损伤进行判定,材料失效后基于CDM中线性软化模型对材料损伤进行演化。模型考虑了复合材料层合板子层的就位效应和剪切非线性行为。对Carlsson的AS4/3501-6缺口拉伸强度试验进行数值模拟。结果表明:分析结果与试验结果吻合良好,证明了该模型能够准确地预测含缺口复合材料层合板面内拉伸强度。      

Failure analysis of multiple delaminated composite plates due to bending and impact

The present work aims at the first ply failure analysis of laminated composite plates with arbitrarily located multiple delaminations subjected to transverse static load as well as impact. The theoretical formulation is based on a simple multiple delamination model. Conventional first order shear deformation is assumed using eight-noded isoparametric quadratic elements to develop the finite element analysis procedure. Composite plates are assumed to contain both single and multiple delaminations. For the case of impact, Newmark time integration algorithm is employed for solving the time dependent multiple equations of the plate and the impactor. Tsai-Wu failure criterion is used to check for failure of the laminate for both the cases. To investigate the first ply failure, parametric studies are made for different cases by varying the size and number of delaminations as well as the stacking sequences and boundary conditions.     

缝合复合材料层板低速冲击损伤数值模拟

建立了缝合复合材料层板在低速冲击载荷下的渐进损伤分析模型。模型中采用空间杆单元模拟缝线的作用;采用三维实体单元模拟缝合层板,通过基于应变描述的Hashin准则,结合相应的材料性能退化方案模拟层板的损伤和演化;采用界面单元模拟层间界面,结合传统的应力失效判据和断裂力学中的应变能释放率准则判断分层的起始和扩展规律。通过对碳800环氧树脂复合材料（T800/5228）层板的数值仿真结果和试验结果相比较,验证了模型的正确性,同时讨论了不同冲击能量下缝合层板的损伤规律。研究结果表明：缝线能够有效地抑制层板的分层损伤扩展;相同冲击能量下缝合与未缝合层板的基体损伤和纤维损伤在厚度分布上相似,缝合层板的损伤都要小于未缝合层板。     

Stress analysis of imperfect composite laminates with an interlaminar bonding theory

Delamination is a major damage mode in laminated composites since it can cause severe structural degradation. Based on an interlaminar shear stress continuity theory and a linear shear slip theory, a so-called Interlayer Shear Slip Theory was presented in a previous study. This theory was verified to be feasible for shearing-mode delamination analysis. However, in order to account for opening-mode delamination in laminated composites, the continuity of interlaminar normal stress and the modelling of normal separation on the composite interface should also be considered. The present study gives a complete discussion on the Interlaminar Bonding Theory. The effects of interlaminar bonding condition on the laminate deformation and stress distribution are also presented. It is concluded from numerical results that the present theory is suitable for analysis of composite laminates with imperfect interfaces.     

复合材料加筋板低速冲击损伤的数值模拟

建立了复合材料加筋板在横向低速冲击载荷作用下的渐进损伤有限元模型。该模型考虑了复合材料加筋板受低速冲击时的纤维断裂、基体开裂及分层脱粘等五种典型的损伤形式, 在层内采用应变描述的失效判据, 结合相应的材料性能退化方案, 通过编写VUMAT用户自定义子程序以实现相应损伤类型的判断和演化。在层间以及筋条与层板间加入界面元, 模拟层间区域的情况, 结合传统的应力失效判据和断裂力学中的能量释放率准则来判断分层损伤的起始和演化规律。通过对数值模拟结果与实验数据的比较, 验证了模型的合理性和有效性。同时探讨了不同位置、不同冲击能量以及含初始损伤(脱粘)等因素对复合材料加筋板低速冲击性能的影响。     

Finite element modeling of delamination by layerwise shell element allowing for interlaminar displacements

This paper presents a novel approach of modeling the delamination phenomenon experienced by laminated composite plate and shell structures by using a previously developed layerwise shell finite element in conjunction with some transformations. This layerwise element is formulated by stacking some single-layered shell elements through a transformation of displacements of the mid-surface of a layer to those on the mid-surface of the laminated composite shell structure. It can accurately model the overall displacements and interlaminar stresses of a laminated composite shell structures whose layers are perfectly (rigidly) bonded. The novelty of the present approach, however, lies in the fact that two different transformations are used so that interlaminar displacements as well as interlaminar stresses can be represented in the finite element model. The transformations allow for displacement mismatches across the normal direction of the layer interfaces (the normal mode of delamination) and between layers (the shear mode). As a result, the proposed methodology can be used to model the open and shear modes of delamination. A two-layered simply supported composite beam and a two-layered simply supported cross-ply square plate are then chosen for numerical studies. These examples demonstrate how the present approach can be applied to accurately model delamination phenomena such as shear slip and normal separation. The paper concludes with suggestions for future work.     

含纤维波纹缺陷复合材料层合板的损伤分析

纤维波纹是复合材料层合板制备过程中的一种常见缺陷,会导致其刚度和强度显著下降,有效地预测含波纹缺陷复合材料层合板的失效强度具有显著的意义。基于此,本文采用解析的方式分别构造了纤维波纹呈正弦起伏与余弦起伏状的复合材料层合板模型。利用该模型,以Tsai-Wu准则作为失效判据,研究了一种含纤维波纹的碳纤维/环氧树脂复合材料层合板在受压情况下的损伤演化过程,得到了碳纤维/环氧树脂复合材料层合板的初始损伤强度。与有限元方法计算得到的损伤位置和损伤强度非常吻合,验证了本文算法的正确性。另外,相比于有限元方法,本文所述计算方法具有模型构造简单、计算效率高等优点,便于快速分析和确定含纤维波纹缺陷复合材料层合板的损伤位置与损伤强度。