Direct Evaluation of Cohesive Law in Mode I of Pinus pinaster by Digital Image Correlation

The direct identification of the cohesive law in pure mode I of Pinus pinaster is addressed in this work. The approach couples the double cantilever beam (DCB) test with digital image correlation (DIC). Wooden beam specimens loaded in the radial-longitudinal (RL) fracture propagation system are used. The strain energy release rate in mode I (G _I) is uniquely determined from the load–displacement curve by means of the compliance-based beam method (CBBM). This method relies on the concept of equivalent elastic crack length (a _eq) and therefore does not require the monitoring of crack propagation during test. DIC measurements are processed with two different purposes. Firstly, the physical evidence of a _eq is discussed with regard to actual estimation of the crack length based on post-processing full-field displacement measurements. Secondly, the crack tip opening displacement in mode I (w _I) is determined from the displacements near the initial crack tip. The cohesive law in mode I (σ _I???w _I) is then identified by numerical differentiation of the G _I???w _I relationship. The methodology and accuracy on this reconstruction are addressed. Moreover, the proposed procedure is validated by finite element analyses including cohesive zone modelling. It is concluded that the proposed data reduction scheme is adequate for assessing the cohesive law in pure mode I of P. pinaster.     

A microsystem for the fracture characterization of polysilicon at the micro-scale

To characterize the effective fracture energy G_IC of polysilicon wafers at room temperature, an on-chip MEMS test structure has been designed and fabricated. The device can provide fatigue pre-cracking at the notch apex and subsequently impose a monotonical load up to failure. The proposed procedure combines the experimental data with outcomes of numerical simulations. A continuously monitored decrease in stiffness of the system is linked to the crack length and the effective fracture energy for the non-standard geometry of the testing device. An average value of G_IC = 12.0 ± 1.8 N m^?1 is found. These values are then used in numerical micro-scale fracture analyses taking into account the material heterogeneity due to the grain structure and reproducing the crack propagation process with a cohesive approach.     

Theoretical development and experimental validation of a thermally dissipative cohesive zone model for dynamic fracture of amorphous polymers

A thermally dissipative cohesive zone model is developed for predicting the temperature increase at the tip of a crack propagating dynamically in a nominally brittle material exhibiting a cohesive-type failure such as crazing. The model assumes that fracture energy supplied to the crack tip region that is in excess of that needed for the creation of new free surfaces during crack advance is converted to heat within the cohesive zone. Bulk dissipation mechanisms, such as plasticity, are not accounted for. Several cohesive traction laws are examined, and the model is then used to make predictions of crack tip heating at various crack propagation speeds in the nominally brittle amorphous polymer PMMA, observed to fail by a crazing-type mechanism. The heating predictions are compared to experimental data where the temperature field surrounding a high speed crack in PMMA was measured. Measurements are made in real time using a multi-point high speed HgCdTe infrared radiation detector array. At the same time as temperature, simultaneous measurement of fracture energy is made by a strain gauge technique, and crack tip speed is monitored through a resistance ladder method. Material strength can be estimated through uniaxial tension tests, thus minimizing the need for parameter fitting in the stress-opening traction law. Excellent agreement between experiments and theory is found for two of the cohesive traction law temperature predictions, but only for the case where a single craze is active during the dynamic fracture of PMMA, i.e. crack tip speed up to approximately 0.2c_R. For higher speed fracture where subsurface damage becomes prominent, the line dissipation model of a cohesive zone is inadequate, and a distributed damage model is needed.     

Adhesive fracture of a lap shear joint

In many respects, adhesive and cohesive fractures are similar. It has been demonstrated in both cases that a Griffith-type energy balance can often be used to predict failure, e.g., crack growth. The only essential difference involves the interpretation of the energy required to create new (adhesive or cohesive) surface area. In the cohesive case, the specific fracture energy γ _c is that required to create a new surface in the same material, while in the adhesive case, the specific fracture energy γ _a is the energy per unit area required to separate different materials. The mechanical analysis, including a stress analysis to determine the strain energy and energy balance in principle remains unchanged. Generally speaking adhesive-bonded joints involve sharp corners or other “singularities” between adjacent materials which act as stress concentrators, particularly if a crack or other sharp imperfection is present or arises at such a location. The Griffith energy approach circumvents the problem of just how large this mathematically infinite stress must be to initiate failure. Recently, this method had been successfully applied to a number of different adhesive geometries; this paper discusses the case of a single-lap shear joint. This geometry is important because the lap-joint test is a common method for comparing adhesive strengths; in addition, the configuration itself is often used in engineering practice. Adhesive fracture is, therefore, compared on the basis of both energy and maximum stress criteria. Experimental data suggest the former to yield more accurate predictions.     

A numerical study on the SEN-TPB test applied to mode I wood fracture characterization

A numerical study involving the single edge notched-three point bending test was methodically performed to evaluate its adequacy for wood fracture characterization under mode I loading. Stress analysis along the ligament length using cohesive zone modeling allowed understating the influence of the compressive stresses induced by bending on the stress profile for geometrically similar specimens with different sizes. The stress relief region induced by the presence of the crack was identified by a stress analysis procedure along the beam length. A data reduction scheme based on the beam theory and on the crack equivalent concept was then developed considering an approach using a rectangular stress relief region. The method allows estimating the Resistance-curve without monitoring the crack length during propagation. Important remarks regarding the aspects which contribute to explain the size effect phenomenon in wood are highlighted in this study. Following the presented procedure the application of the single edge notched-three point bending test for wood fracture characterization under mode I has become considerably user-friendlier.     

On the determination of the cohesive zone properties of an adhesive layer from the analysis of the wedge-peel test

An extensive numerical study of the mechanics of the “wedge-peel test” is performed in order to analyze the mode I steady state debonding of a sandwich structure made of two thin plastically deforming metallic plates bonded with an adhesive. The constitutive response of the metallic plates is modeled by J₂ flow theory, and the behavior of the adhesive layer is represented with a cohesive zone model characterized by a maximum separation stress and the fracture energy. A steady-state finite element code accounting for finite rotation has been developed for the analysis of this problem. Calculations performed with the steady-state formulation are shown to be much faster than simulations involving both crack initiation and propagation within a standard, non-steady-state code. The goal of this study is to relate the measurable parameters of the test to the corresponding fracture process zone characteristics for a representative range of adherent properties and test conditions. An improved beam bending model for the energy release rate is assessed by comparison with the numerical results. Two procedures are proposed for identifying the cohesive zone parameters from experimental measurements.     

Numerical analysis of the dual actuator load test applied to fracture characterization of bonded joints

The dual actuator load test was numerically analyzed in order to assess its adequacy for fracture characterization of bonded joints under different mixed-mode loading conditions. This test enables asymmetric loading of double cantilever beam specimens, thus providing a large range of mixed-mode combinations. A new data reduction scheme based on specimen compliance, beam theory and crack equivalent concept was proposed to overcome several difficulties inherent to the test. The method assumes that the dual actuator test can be viewed as a combination of the double cantilever beam and end loaded split tests, which are used for pure modes I and II fracture characterization, respectively. A numerical analysis including a cohesive mixed-mode damage model was performed considering different mixed-mode loading conditions to evaluate the test performance. Some conclusions were drawn about the advantages and drawbacks of the test.     

A new quasi-continuum constitutive model for crack growth in an isotropic solid

A new quasi-continuum constitutive model is established based on the randomized cohesive bonds model proposed by Gao and Klein (1998). This model bridges the microscopic discrete constitution characters and the macroscopic mechanical properties of material. In the presented constitutive model, both the bond stretch energy potential and the rotation energy potential are considered, which makes the presented constitutive model applicable to different Poisson-ratio and Young's modulus materials. By establishing a phenomenological bond stiffness function according to the complete stress–strain relationship of uniaxial tension test, the fracture criterion is directly incorporated into the constitutive model. The method requires no external fracture criterion when simulating fracture initiation and propagation, which brings convenience in the numerical simulation. At last, the presented constitutive model is applied to an example of crack growth in an isotropic solid.     

内聚力模型裂纹问题分析的解析奇异单元

内聚力模型已经被广泛应用于需要考虑断裂过程区的裂纹问题当中,然而常用的数值方法应用于分析内聚力模型裂纹问题时还存在着一些不足,比如不能准确的给出断裂过程区的长度、需要网格加密等。为了克服这些缺点,论文构造了一个新型的解析奇异单元,并将之应用于基于内聚力模型的裂纹分析当中。首先将虚拟裂纹表面处的内聚力用拉格拉日插值的方法近似表示为多项式的形式,而多项式表示的内聚力所对应的特解可以被解析地给出。然后利用一个简单的迭代分析,基于内聚力模型的裂纹问题就可以被模拟出来了。最后,给出二个数值算例来证明本文方法的有效性。     

多裂纹扩展分析的边界元方法

采用边界元数值模拟和即时等效材料常数计算相结合的办法，只需模拟一个裂纹的扩展情况便可预测裂纹体的整体响应。针对准脆性材料的特点，采用粘性裂纹模型模拟裂纹开裂行为；采用二次裂纹扩展量作为增量控制变量，避免了软化及失稳分析中用力或位移作控制变量时遇到的困难。针对二交裂纹扩展路径未知情况，给出了预测和修正裂纹开裂界面的迭代技术，分析计算了含多个规则分布裂纹石膏板受压时的响应，并与实验结果进行了比较。结果表明该文方法的可行性与有效性。     

Disk-shaped compact tension test for asphalt concrete fracture

A disk-shaped compact tension (DC(T)) test has been developed as a practical method for obtaining the fracture energy of asphalt concrete. The main purpose of the development of this specimen geometry is the ability to test cylindrical cores obtained from in-place asphalt concrete pavements or gyratory-compacted specimens fabricated during the mixture design process. A suitable specimen geometry was developed using the ASTM E399 standard for compact tension testing of metals as a starting point. After finalizing the specimen geometry, a typical asphalt concrete surface mixture was tested at various temperatures and loading rates to evaluate the proposed DC(T) configuration. The variability of the fracture energy obtained from the DC(T) geometry was found to be comparable with the variability associated with other fracture tests for asphalt concrete. The ability of the test to detect changes in the fracture energy with the various testing conditions (temperature and loading rate) was the benchmark for determining the potential of using the DC(T) geometry. The test has the capability to capture the transition of asphalt concrete from a brittle material at low temperatures to a more ductile material at higher temperatures. Because testing was conducted on ungrooved specimens, special care was taken to quantify deviations of the crack path from the pure mode I crack path. An analysis of variance of test data revealed that the prototype DC(T) can detect statistical differences in fracture energy resulting for tests conducted across a useful range of test temperatures and loading rates. This specific analysis also indicated that fracture energy is not correlated to crack deviation angle. This paper also provides an overview of ongoing work integrating experimental results and observations with numerical analysis by means of a cohesive zone model tailored for asphalt concrete fracture behavior.     

Three-dimensional cohesive fracture modeling of non-planar crack growth using adaptive FE technique

In this paper, the three-dimensional adaptive finite element modeling is presented for cohesive fracture analysis of non-planer crack growth. The technique is performed based on the Zienkiewicz–Zhu error estimator by employing the modified superconvergent patch recovery procedure for the stress recovery. The Espinosa–Zavattieri bilinear constitutive equation is used to describe the cohesive tractions and displacement jumps. The 3D cohesive fracture element is employed to simulate the crack growth in a non-planar curved pattern. The crack growth criterion is proposed in terms of the principal stress and its direction. Finally, several numerical examples are analyzed to demonstrate the validity and capability of proposed computational algorithm. The predicted crack growth simulation and corresponding load-displacement curves are compared with the experimental and other numerical results reported in literature.     

粘聚裂纹扩展的强化有限元h型网格自适应模拟

非连续变形分析和非规则节点处理是基于单元细划的粘聚裂纹扩展网格自适应模拟的关键。首先,利用强化有限单元法中数学单元和物理单元分离的特点,通过引入过渡单元,将适用于非连续变形描述的数学模式覆盖法和方便处理非规则节点的物理模式重构法结合,提出了强化有限单元法的统一关联法则,并导出了相应的单元列式。其次,基于数学裂纹尖端影响域和裂尖单元尺寸,提出了基于强化有限单元法的粘聚裂纹扩展过程模拟的h型网格自适应策略。最后,通过两个算例验证了本文方法的合理性和有效性。     

Cohesive fracture simulation and failure modes of FRP–concrete bonded interfaces

A work-of-fracture method using three-point bend beam (3PBB) specimen, commonly employed to determine the fracture energy of concrete, is adapted to evaluate the mode-I cohesive fracture of fiber reinforced plastic (FRP) composite–concrete adhesively bonded interfaces. In this study, a bilinear damage cohesive zone model (CZM) is used to simulate cohesive fracture of FRP–concrete bonded interfaces. The interface cohesive process damage model is proposed to simulate the adhesive–concrete interface debonding; while a tensile plastic damage model is used to account for the cohesive cracking of concrete near the bond line. The influences of the important interface parameters, such as the interface cohesive strength, concrete tensile strength, critical interface energy, and concrete fracture energy, on the interface failure modes and load-carrying capacity are discussed in detail through a numerical finite element parametric study. The results of numerical simulations indicate that there is a transition of the failure modes controlling the interface fracture process. Three failure modes in the mode-I fracture of FRP–concrete interface bond are identified: (1) complete adhesive–concrete interface debonding (a weak bond), (2) complete concrete cohesive cracking near the bond line (a strong bond), and (3) a combined failure of interface debonding and concrete cohesive cracking. With the change of interface parameters, the transition of failure modes from interface debonding to concrete cohesive cracking is captured, and such a transition cannot be revealed by using a conventional fracture mechanics-based approach, in which only an energy criterion for fracture is employed. The proposed cohesive damage models for the interface and concrete combined with the numerical finite element simulation can be used to analyze the interface fracture process, predict the load-carrying capacity and ductility, and optimize the interface design, and they can further shed new light on the interface failure modes and transition mechanism which emulate the practical application.     

The surface-forming energy release rate based fracture criterion for elastic–plastic crack propagation

The J-integral based criterion is widely used in elastic–plastic fracture mechanics. However, it is not rigorously applicable when plastic unloading appears during crack propagation. One difficulty is that the energy density with plastic unloading in the J-integral cannot be defined unambiguously. In this paper, we alternatively start from the analysis on the power balance, and propose a surface-forming energy release rate (ERR), which represents the energy available for separating the crack surfaces during the crack propagation and excludes the loading-mode-dependent plastic dissipation. Therefore the surface-forming ERR based fracture criterion has wider applicability, including elastic–plastic crack propagation problems. Several formulae are derived for calculating the surface-forming ERR. From the most concise formula, it is interesting to note that the surface-forming ERR can be computed using only the stress and deformation of the current moment, and the definition of the energy density or work density is avoided. When an infinitesimal contour is chosen, the expression can be further simplified. For any fracture behaviors, the surface-forming ERR is proven to be path-independent, and the path-independence of its constituent term, so-called J_s-integral, is also investigated. The physical meanings and applicability of the proposed surface-forming ERR, traditional ERR, J_s-integral and J-integral are compared and discussed. Besides, we give an interpretation of Rice paradox by comparing the cohesive fracture model and the surface-forming ERR based fracture criterion.     

金属材料层裂破坏的内聚力模型

本文把内聚力单元嵌入到连续介质有限元单元之间,构建了一个层裂破坏的内聚力模型,以计及层裂破坏过程中能量耗散行为。采用该模型对平板撞击条件下的20号钢层裂实验进行了数值模拟研究,重点讨论了内聚力模型特征参数对计算结果的影响规律。研究结果表明采用指数型损伤演化行为的内聚力模型可以较好地描述弹塑性材料层裂破坏过程中的非线性能量耗散行为。利用一发实测自由面速度波剖面对计算结果进行对比校准,可确定内聚力模型特征参数。该特征参数可同样成功地预示不同撞击速度下的层裂实验,获得的模拟曲线与实验曲线之间符合程度很好,特别是自由面速度“回跳”后波形振荡周期和幅值与实验结果非常接近。这表明了内聚力模型在描述层裂过程中能量耗散行为方面具有较好适用性,并且不难由简单实验标定相关的特征参数。     

Cohesive zone laws for fatigue crack growth: Numerical field projection of the micromechanical damage process in an elasto-plastic medium

Cohesive zone failure models are widely used to simulate fatigue crack propagation under cyclic loading, but the model parameters are phenomenological and are not closely tied to the underlying micromechanics of the problem. In this paper, we will inversely extract the cohesive zone laws for fatigue crack growth in an elasto-plastic ductile solid using a field projection method (FPM), which projects the equivalent tractions and separations at the cohesive crack-tip from field information outside the process zone. In our small-scale yielding model, a single row of discrete voids is deployed directly ahead of a crack in an elasto-plastic medium subjected to cyclic mode I K-field loading. Damage accumulation under cyclic loading is captured by the growth of voids within the micro-voiding zone ahead of the crack, while the evolution of the cohesive zone law representing the micro-voiding zone is inversely extracted via the FPM. We show that the field-projected cohesive zone law captures the essential micromechanisms of fatigue crack growth in the ductile medium: from loading and unloading hysteresis caused by void growth and plastic hardening, to the softening damage locus associated with crack propagation via a void by void growth mechanism. The results demonstrate the effectiveness of the FPM in obtaining a micromechanics-based cohesive zone law in-place of phenomenological models, which opens the way for a unified treatment of fatigue crack problems.     

Analysis of crack growth and crack-tip plasticity in ductile materials using cohesive zone models

Crack initiation and crack growth resistance in elastic plastic materials, dominated by crack-tip plasticity are analyzed with the crack modeled as a cohesive zone. Two different types (exponential and bilinear) of cohesive zone models (CZMs) have been used to represent the mechanical behavior of the cohesive zones. In this work, it is suggested that different forms of CZMs (e.g., exponential, bilinear) are the manifestations of different micromechanisms-based inelastic processes that participate in dissipating energy during the fracture process and each form is specific to each material system. It is postulated that the total energy release rate comprises the plastic dissipation rate in the bounding material and the separation energy rate within the fracture process zone, the latter is determined by CZMs. The total energy release rate then becomes a function of the material properties (e.g., yield strength, strain hardening exponent) and cohesive properties of the fracture process zone (e.g., cohesive strength and cohesive energy), and the form of cohesive zone model (CZM) that determines the rate of energy dissipation in the forward and wake regions of the crack. The effects of material parameters, cohesive zone parameters as well as the form/shape of CZMs in predicting the crack growth resistance and the size of plastic zone (SPZ) surrounding the crack tip are systematically examined. It is found that in addition to the cohesive strength and cohesive energy, the form (shape) of the traction–separation law of CZM plays a very critical role in determining the crack growth resistance (R-curve) of a given material. It is further observed that the shape of the CZM corresponds to inelastic processes active in the forward and wake regions of the crack, and has a profound influence on the R-curve and SPZ.     

Effects of near-tip rotation on pre-buckle crack growth of compressed beams bonded to a rigid substrate

The macroscopic pre-cracked line scratch test (MPLST), in which a debonded edge of a film is loaded in in-plane compression, has been modeled as a generic, coupled fracture–buckle problem using simple beam theory. Near crack-tip beam rotation (also called root rotation in literature), which always exists due to the eccentric loading in this type of test, has been incorporated into the governing equations. An analytical solution to the augmented problem has been derived. It is found that the near-tip rotation can introduce pre-buckle bending in the film. One important consequence of this pre-buckle bending is that it leads to the reduction of the critical buckling condition. This agrees well with the results of [Int. J. Fract. 113 (2002) 39] obtained by solving the full elastic field near the crack-tip. Furthermore, the pre-buckle bending moment at crack-tip remains negative (leading to crack closure) as long as the pre-buckle crack length is small, but it becomes positive (leading to crack opening) at larger pre-buckle crack length. The negative bending moment causes the crack-tip energy release rate to decrease as the crack propagates, which results in a stable pre-buckle crack growth. Once it becomes positive, however, the bending moment causes crack-tip energy release rate to increase rapidly as crack length increases and hence leads to an unstable (pre-buckle) crack growth. Further, the nominal phase angle is initially larger than the classic prediction of 52.1° owing to the existence of the negative crack-tip bending moment, but it drops quickly upon approaching the buckle point. All these results are confirmed by a rigorous 2D FEM calculation using cohesive zone modeling (CZM) approach. Finally the derived analytical solution has been used to analyze a set of PLST data reported in the literature. It has been demonstrated that plasticity in the adhesive layer and in the bonded film is responsible for the strong R-curve toughening characteristics in the deduced interface toughness data. It has also been shown that, once the deduced interface toughness is incorporated into a CZM simulation, both the axial loading and buckling point can be accurately predicted.