Analysis of experimental factors in elastic–plastic small specimen mixed-mode I-II fracture mechanical testing

The quality of experimental fracture resistance testing results in mixed-mode I-II loading is more than questionable in several cases. This study describes efforts to gain consistent results with respect to mixed-mode I-II fracture resistance curve determination when working with elastic–plastic materials. The entire mixed-mode I-II field is evaluated, i.e. both numerical and experimental factors are considered the focus being on the asymmetric four-point bend set-up. Several error prone features are presented, and minimization of their effects on quantitative fracture resistance assessment considered. The results indicate that through a careful evaluation of the stages in experimental testing and numerical analysis valid, material characterizing, fracture toughness results can be obtained.     

An investigation into the mixed-mode delamination growth in unidirectional T800/924C laminates

This study presents the results of experimental investigations and numerical simulation on mixed-mode I/II delamination growth initiated from an artificial transverse notch. Specimens made of unidirectional carbon fiber epoxy (T800/924C) composite have been tested under three-point-bend condition. A finite element procedure has been introduced to model 3-D stable delamination growth in the specimen to generate numerical growth data including loads, displacements, delamination lengths, and the growing crack front shapes. The simulation method uses strain energy release rate criterion in conjunction with a moving mesh facility. It is shown that very good compatibility exists between experimental and numerical results. A finite element-based data reduction method is then described as an application of the simulation procedure. Based on the obtained results, it is stated that this bending specimen can effectively be used in practice to study the mixed-mode crack growth and to measure interlaminar fracture toughness of unidirectional laminates.     

铺层方向和裂纹混合比对复合材料层压板混合型断裂韧性影响的试验研究

试验研究了复合材料层压板的铺层方向以及裂纹混合比对层间裂纹分层扩展的影响规律。试验结果显示: 在非0°单向板的 Ⅰ 型层间裂纹分层扩展过程中, 会出现层间裂纹穿过分层开裂面的铺层而偏离到相邻铺层间扩展的现象, 而0°铺层具有阻止该裂纹偏离扩展的作用; 在不同裂纹混合比的层压板分层开裂试验中, 相应的0°单向板的断裂韧性均可以作为下限值而偏安全; 混合断裂韧性( Ⅰ 型断裂韧性+ Ⅱ 型断裂韧性)随着裂纹混合比的变化呈现类似正弦曲线的变化规律。      

Effects of core machining configuration on the debonding toughness of foam core sandwich panels

Core machining is often applied to improve the formativeness of foam core and the manufacturing effectiveness of sandwich panels. This paper investigates the effects of core machining configuration on the interfacial debonding toughness of foam core sandwich panels fabricated by vacuum-assisted resin transfer molding process. Several machining configurations are conducted to foam core, and skin–core debonding toughness of fabricated sandwich panels is evaluated using double-cantilever-beam tests. The sandwich panels with core cuts exhibited higher apparent fracture toughness than the panels without core cut, specifically in the case of perforated core. The relationship between core machining configuration and measured fracture toughness is discussed based on the experimental observations and the numerical analyses of energy release rates.     

On the fracture toughness anisotropy of mechanically poled ferroelectric ceramics

In this paper an incremental constitutive theory for the deformation due to switching in ferroelectrics is applied to predict the fracture toughness anisotropy in these materials after mechanical poling. Mechanical poling of an initially unpoled specimen differs from electrical poling in that only mechanical stresses are applied to the material. Therefore, no electrical polarization can develop. After mechanical poling, for example by a uniaxial applied stress, the fracture toughness of a ferroelectric ceramic for cracks running parallel or orthogonal to the poling direction will differ. Finite element computations of the steady crack growth process have been carried out to quantify these differences. Results are generated for a range of constitutive properties for three crack growth directions with respect to the initial mechanical poling direction. The results are discussed in relation to available experimental data and to the toughness anisotropy due to electrical poling.     

On the characteristic distance and minimum fracture toughness for cleavage fracture in a C-Mn steel

This study makes a further investigation on the characteristic distance, minimum fracture toughness and its temperature dependence for cleavage fracture in a C-Mn steel by the detailed finite element analysis combined with experimental observation and measurement. Results show that there is a minimum active zone for cleavage initiation, and the minimum fracture toughness of steel results from the minimum active zone necessary. Corresponding to the minimum fracture toughness, the cleavage fracture ahead of a crack tip can only initiate in a distance range from the minimum distance X_fmin determined by the lower boundary of the active zone to the maximum distance X_fmax determined by its upper boundary. The reason for the occurrence of the minimum active zone and the factors influencing it are analyzed. The temperature dependence of the characteristic distance and minimum fracture toughness and its mechanism are also discussed.     

On the impact response of sandwich composites with cores of balsa wood and PVC foam

This paper presents an experimental investigation on impact response of sandwich composite panels with PVC foam core and balsa wood core. A number of tests were performed under various impact energies. Damage process of the sandwich composites is analyzed from cross-examining load–deflection curves, energy profile diagrams and the damaged specimens. The primary damage modes observed are; fiber fractures at upper and lower skins, delaminations between adjacent glass–epoxy layers, core shear fractures, and face/core debonding. After visual inspection of the top and bottom face-sheets, initial examination, damage mechanisms at the interior layers and cores were ascertained through destructive analysis, i.e. sectioning by an abrasive water-jet machine, of samples. In addition to the single impacts, repeated impact response of the samples is also investigated.     

Experimental and computational investigation of three-dimensional mixed-mode fatigue

Experimental and computational methods were developed to model three-dimensional (3-D) mixed-mode crack growth under fatigue loading with the objective of evaluating proposed 3-D fracture criteria. The experiments utilized 7075-T73 aluminium forgings cut into modified ASTM E740 surface crack specimens with pre-cracks orientated at angles of 30, 45 and 60° in separate tests. The progress of the evolving fatigue crack was monitored in real time using an automated visualization system. In addition, the amplitude of the loading was increased at prescribed intervals to mark the location of the 3-D crack front for post-test inspection. In order to evaluate proposed crack growth equations, computer simulations of the experiments were conducted using a 3-D fracture model based on the surface integral method. An automatic mesher advanced the crack front by adding a ring of elements consistent with local application of fracture criteria governing rate and direction of growth. Comparisons of the computational and experimental results showed that the best correlation was obtained when K _II and K _III were incorporated in the growth rate equations.     

空心微球/环氧树脂复合泡沫塑料的抗压性能与破坏机制

以环氧树脂为基体, 不同粒径空心玻璃微球为填充体, 制备了轻质高强复合泡沫塑料。通过单轴准静态压缩试验研究了空心微球的粒径大小对复合泡沫塑料的抗压性能的影响, 并采用SEM对复合泡沫塑料的微观结构进行观测。通过随机空间分布法建立了空心玻璃微球/环氧树脂复合泡沫塑料的实体模型, 并且使用有限元分析软件对复合泡沫塑料在1 kPa载荷下的应力分布进行了分析。结果表明, 在相同体积含量下, 当空心微球的粒径从30 μm增大到120 μm时, 复合泡沫塑料的抗压强度无明显变化。有限元分析的结果表明, 在复合泡沫塑料中主要承载部分为空心微球, 空心微球上的应力大于树脂基体上的应力。最大应力分布在空心微球的内壁, 结合SEM图像可推测, 空心微球在破裂之前受到充分的挤压, 并且从内壁产生裂纹。     

Removing mesh bias in mixed-mode cohesive fracture simulation with stress recovery and domain integral

To remove mesh bias and provide an accurate crack path representation in mixed-mode investigation, a novel stress recovery technique is proposed in conjunction with a domain integral and element splits. Based on a domain integral and stress recovery technique, a maximum strain energy release rate is estimated to determine a crack path direction. Then, for a given crack path direction, continuum elements are split, and a cohesive surface element is adaptively inserted. One notes that the proposed stress recovery technique provides a more accurate stress field than a standard stress evaluation procedure. The proposed computational framework is verified and validated by solving mode-I and mixed-mode examples. Computational results demonstrate that the domain integral with the stress recovery accurately evaluates a crack path, even with a lower-quality mesh and under a biaxial stress state. Furthermore, the cohesive surface element approach, with the element split in conjunction with the stress recovery and the domain integral, predicts mixed-mode fracture behaviors while removing mesh bias in the crack path representation. Additionally, the condition numbers of stiffness matrices are within the same order of magnitude during cohesive fracture simulation.     

Deformation localisation modelling of polymer foam microstructure under compression: A new approach by discrete element modelling

A discrete element model (DEM) has been developed to represent the behaviour of the microscopic structure of polymer cellular material, consisting of closed-cells. In DEM, the polymer foam is represented as an assembly of particles which model the closed-cells. The behaviour of the particle is based on the Gibson model and depends on morphologic and mechanical parameters. The present numerical study demonstrates the effect of deformation localisation on the microstructure. It is noted that the cell morphologic parameters and the distribution of various size cells in the specimen have a significant influence of the local deformation. The effect of macroscopic faults is also studied.     

Mixed-mode fracture characterization of adhesive joints

A novel load jig is presented which allows mixed-mode fracture testing of adhesive joints and composite laminates over the entire range from mode I to mode II, by using a single equal adherend double-cantilever-beam specimen. Experiments performed with the load jig showed that G_IIC was approximately three times higher than G_IC for the tested adhesive system consisting of FPL-etched 7075-T6 aluminium adherends bonded with Cybond 4523GB (American Cyanamid) epoxy adhesive. Experimental data showed that G_C was independent of crack length and that there was no dependence of G_IC on adherend thickness. Comparison of G_IIC values obtained by using the load jig to test conventional end notch flexure (ENF) specimens indicated that there are relatively small friction effects between crack faces in mode II testing of ENF specimens. The experimental data were also used to evaluate three different analytical techniques for the mode partitioning of unequal adherend specimens.     

Adaptive finite element analysis of mixed-mode fracture problems containing multiple crack-tips with an automatic mesh generator

A fully automatic advancing front type mesh generator to take care of crack problems has been presented. It is coupled with the Zienkiewicz and Zhu error estimator and the refinement methodology depends on the concept of strain energy concentration for completely automatic adaptive analysis of mixed-mode crack problems. For the first time energy based path independent M ₁-integral has been used to extract mixed-mode stress intensity factors in randomly changing quadratic triangular meshes. To fulfill the objective of automatic adaptive procedures, an approach has been suggested and validated for generation of integration paths automatically without user intervention. Stress intensity factors have been obtained within engineering accuracy.     

Constitutive models for cohesive zones in mixed-mode fracture of plain concrete

Discrete mixed-mode fracture (modes I and II) of plain concrete is investigated using a coupled and an uncoupled cohesive zone constitutive model in a finite element context. Fracture surfaces are confined to inter-element boundaries that are not necessarily coincident with the actual fracture surfaces. For this reason, traction components on the cohesive zone do not correspond to actual values either. In this work is demonstrated that only the coupled model is able to cope with these spurious traction components, that must decrease with crack opening. It is shown also that, in this regard, the key variable is the plastic potential adopted in the integration of tractions. Three mixed-mode fracture examples were tested in this work: a three-point single-edge notched beam, double-edge notched plates under variable lateral and normal deformation and four-point double-edge notched beams. A good fitting with experiments was obtained only for the coupled model. Mode II parameters can change in a large range without noticeable change in results, at least in the tested examples.     

Evaluation of the dynamic properties of PVC foams under flexural vibrations

The paper presents an investigation of the damping of PVC foams under flexural vibrations of clamped-free beams. The PVC foams are constrained by two aluminium beams and different densities of the PVC foams are studied. An experimental investigation is implemented using an impulse technique. The natural frequencies and the damping of the beams are modelled by using a finite element analysis based on the sandwich theory. Next, the numerical and experimental results are used to derive the shear modulus and the damping of PVC foams as functions of the frequency. Finally, the experimental investigation and the developed modelling show how the damping of aluminium–foam beams must be corrected to estimate the damping of PVC foams.     

An FEM study on crack tip blunting in ductile fracture initiation

Ductile fracture is initiated by void nucleation at a characteristic distance (I_c) from the crack tip and propagated by void growth followed by coalescence with the tip. The earlier concepts expressed I_c in terms of grain size or inter-particle distance because grain and particle boundaries form potential sites for void nucleation. However, Srinivas et al. (1994) observed nucleation of such voids even inside the crack tip grains in a nominally particle free Armco iron. In an attempt to achieve a unified understanding of these observations, typical crack-tip blunting prior to ductile fracture in a standard C(T) specimen (Mode I) was studied using a finite element method (FEM) supporting large elasto-plastic deformation and material rotation. Using a set of experimental data on Armco iron specimens of different grain sizes, it is shown that none of the locations of the maxima of the parameters stress, strain and strain energy density correspond to I_c. Nevertheless, the size of the zone of intense plastic deformation, as calculated from the strain energy density distribution ahead of the crack tip in the crack plane, compares well with the experimentally measured I_c. The integral of the strain energy density variation from the crack tip to the location of void nucleation is found to be linearly proportional to J_IC. Using this result, an expression is arrived at relating I_c to J_IC and further extended to CTOD_c.     

Experimental Characterisation and Numerical Modelling of Hexagonal Honeycomb Cellular Solids under Multi‐axial Loading

Abstract: Cellular solids are becoming increasingly popular for sandwich core and energy‐absorbing applications in many automotive and other transportation structures. This paper investigates experimentally and numerically the strength and post‐failure energy absorption of a popular hexagonal aluminium honeycomb material under multi‐axial loading conditions. For the experimental work, an improved Arcan test apparatus is used so that interaction of multi‐axial compression and shear loading on failure and crushing may be studied; optical measuring methods are used to extract deformation data. In addition, experimental work to characterise the material with pre‐deformation in the in‐plane directions has also been conducted. This experimental work provides input for computational modelling of the material and two alternative modelling approaches have been investigated. First, a three‐dimensional anisotropic, elastic–plastic model, with coupling of loading components is used to represent the material at the macro‐level and, second, a meso‐modelling approach using a fine shell representation of the thin‐walled honeycomb cellular structure is applied. For practical analysis of large‐scale structures, the former approach is computationally efficient and can reasonably treat the most important failure and crush characteristics of the material. However, for more accurate analysis, particularly in the case of complex non‐proportional loading, the meso‐shell model may provide a more realistic solution.     

Fatigue fracture in plates in tension and out-of-plane shear

Straight cracks near a stiffening element, or curved cracks, in a pressurized shell can be subjected to out-of-plane tearing stresses in addition to normal tensile stresses due to the membrane stresses in the shell. To predict the rate of fatigue crack growth in such situations a theory and a crack growth rate correlation are needed. Such loadings are modelled as a superposition of plane stress tensile fracture (mode I) and Kirchhoff plate theory shearing fracture (mode 2). Finite element analyses using shell elements are used to compute the energy release rate and stress intensity factors associated with the loading. Three fatigue crack growth rate experiments were carried out on sheets of 2024-T3 aluminium alloy loaded in tension and torsion. The first set of experiments is constant amplitude fatigue crack growth tests. The second consists of experiments where crack closure is artificially eliminated to determine the rate of crack growth in the absence of crack face contact. The third is a set of constant stress intensity factor amplitude tests. The results all show that as the crack grows extensive crack face contact occurs, retarding crack growth. In the absence of crack face contact, however, the addition of out-of-plane shear loading increases the crack growth rate substantially.     

Continuum shape sensitivity analysis of mixed-mode fracture using fractal finite element method

This paper presents a new fractal finite element based method for continuum-based shape sensitivity analysis for a crack in a homogeneous, isotropic, and two-dimensional linear-elastic body subject to mixed-mode (modes I and II) loading conditions. The method is based on the material derivative concept of continuum mechanics, and direct differentiation. Unlike virtual crack extension techniques, no mesh perturbation is needed in the proposed method to calculate the sensitivity of stress-intensity factors. Since the governing variational equation is differentiated prior to the process of discretization, the resulting sensitivity equations predicts the first-order sensitivity of J-integral or mode-I and mode-II stress-intensity factors, K_I and K_II, more efficiently and accurately than the finite-difference methods. Unlike the integral based methods such as J-integral or M-integral no special finite elements and post-processing are needed to determine the first-order sensitivity of J-integral or K_I and K_II. Also a parametric study is carried out to examine the effects of the similarity ratio, the number of transformation terms, and the integration order on the quality of the numerical solutions. Four numerical examples which include both mode-I and mixed-mode problems, are presented to calculate the first-order derivative of the J-integral or stress-intensity factors. The results show that first-order sensitivities of J-integral or stress-intensity factors obtained using the proposed method are in excellent agreement with the reference solutions obtained using the finite-difference method for the structural and crack geometries considered in this study.