Dynamic fracture rate of Charpy V-notch specimen

Considered in this work is the dynamic loading rate effect on the fracture of pre-notched beam specimens. Four different dynamic loading rates for the same total work are analyzed using a three point bent specimen as specified by ASTM E-23, generally known as the Charpy simple-beam impact test. It will be referred to herein as the Charpy V-notch (CVN) configuration. As an example, the rate at which energy is applied dynamically to initiate fracture for the HY-80 casting material is determined. It is not sufficient to characterize the dynamic fracture behavior of material in units of foot-pound. What controls dynamic fracture is the rate of energy dissipated in the material damage process. The current approach of critical dynamic stress intensity factor and/or Charpy foot-pound has no theoretical basis and can lead to unreliable predictions when used in structural applications.     

An investigation of the losipescu and asymmetrical four-point bend tests

The Iosipescu shear test, utilizing a notched specimen in bending and a modification—the asymmetrical four-point bend (AFPB) test—were evaluated as shear tests for composites. This paper summarizes the results of an extensive numerical and experimental investigation of the Iosipescu and AFPB test methods. Finite-element analyses were conducted to assess the influence of notch parameters and load locations on the stress state in the specimen. The shear moduli and the shear strengths were experimentally measured for a quasiisotropic graphite/epoxy laminate using both the Iosipescu and the AFPB test methods. The tests were conducted for various combinations of notch parameters and load locations. The test results indicate that changes in the notch geometry and load locations aimed at improving the stress distribution in the test section resulted in unexpected changes in the failure mode. Paper was presented at the 1985 SEM Spring Conference on Experimental Mechanics held in Las Vegas, NV on June 9–14.     

Dynamic compression-shear response of brittle materials with specimen recovery

A new configuration for compression-shear soft-recovery experiments is presented. This technique is used to investigate various failure mechanisms during dynamic multiaxial loading of an Al₂O₃/SiC nanocomposite and TiB₂. Velocity profiles of the target surface are measured with a variable sensitivity displacement interferometer, yielding normal and transverse velocity-time histories. A dynamic shear stress of approximately 280 MPa is obtained, in the Al₂O₃/SiC nanocomposite, for an imposed axial stress of about 3.45 GPa on a 540 m thick sample. This dynamic shear stress is well below the value predicted by elastic wave propagation theory. This could be the result of stress-induced damage and inelasticity in the bulk of the sample or inelasticity on the sample surface due to frictional sliding. To gain further insight into the possible failure mechanisms, an investigation of compression-shear recovery techniques, with simultaneous trapping of longitudinal and lateral release waves, is conducted.     

基于COMSOL的脆性材料相场断裂模型

相场法通过一系列微分方程描述材料断裂过程,避免了繁琐的裂纹面追踪,在模拟裂纹的萌生、扩展和分叉等方面具有优势。介绍了基于相场法的脆性材料断裂模型,给出了脆性材料断裂问题相场法控制方程的推导过程,提出了基于分步迭代法在COMSOL中实现脆性材料相场断裂模型的方法。再现了脆性材料单元模型和单边缺口平板受拉及受剪作用下的开裂过程,模拟的裂纹扩展路径与已有文献的结果相近,验证了程序的合理性。针对脆性材料相场断裂模型包含的诸多参数,采用Morris法对影响荷载-位移关系的脆性材料断裂模型参数进行了全局敏感性分析,结果表明,杨氏模量(E)、临界能量释放率(G_c)和位移增量(Δu_x)是影响模型荷载-位移关系输出结果的主要参数。基于COMSOL实现的相场断裂模型能够有效模拟脆性材料的裂纹萌生和扩展断裂过程,模型参数E,G_c和Δu_x对材料断裂性能的提升或模型参数反演效率的提高具有重要影响。     

Stable growth of fracture in brittle aggregate materials

Fracture of concrete is analyzed by combining the resistance curve (R-curve) approach with linearly elastic solutions for the energy release rate resulting from the quasi-static crack model of Wnuk, analogous to the D-BCS model of a stationary crack used in describing quasi-brittle fracture in metals. The R-curve, representing the crack length dependence of the energy consumed per unit fracture extension, is calculated using the concept of the energy separation rate associated with a finite crack growth steps. To simplify calculations, the tensile stress transmitted across the nonlinear zone ahead of the fracture front is assumed to be uniformly distributed over the entire nonlinear zone, even though in reality it must be a gradually declining stress resulting in strain-softening; and an infinite elastic medium loaded at infinity is assumed. These assumptions permit an easy solution with the help of Green's function for an infinite elastic medium. Application to bodies of finite size then requires assuming the nonlinear zone (fracture process zone) to be negligible with regard to specimen dimensions, crack length and ligament length. Even though this assumption is not always realistic, the end results, which are of practical importance, appear reasonable. The analysis leads to a nonlinear first-order ordinary differential equation for the R-curve, which is integrated numerically. The R-curves calculated in this manner can be closely fitted to data from previous fracture tests. Only two parameters, characterizing the initial and the final lengths of the nonlinear zone, need to be adjusted to test data.     

On determination of mode II fracture toughness using semi-circular bend specimen

The cracked semi-circular specimen subjected to three-point bending has been recognized as an appropriate test specimen for conducting mode I, mode II and mixed mode I/II fracture tests in brittle materials. The manufacturing and pre-cracking of the specimen are simple. No complicated loading fixture is also required for a fracture test. However, almost all of the theoretical criteria available for mixed mode brittle fracture fail to predict the experimentally determined mode II fracture toughness obtained from the semi-circular bend (SCB) specimen. In this paper, a modified maximum tangential stress criterion is used for calculating mode II fracture toughness K_IIc in terms of mode I fracture toughness K_Ic. The modified criterion is used for predicting the reported values of mode II fracture toughness for two brittle materials: a rock material (Johnstone) and a brittle polymer (PMMA). It is shown that the modified criterion provides very good predictions for experimental results.     

Scattered fracture of porous materials with brittle skeleton

A model of damage accumulation in a porous medium with a brittle skeleton saturated with a compressible fluid is formulated in the isothermal approximation. The model takes account of the skeleton elastic energy transformation into the surface energy of microcracks. In the case of arbitrary deformations of an anisotropic material, constitutive equations are obtained in a general form that is necessary and sufficient for the objectivity and thermodynamic consistency principles to be satisfied. We also formulate the kinetics equation ensuring that the scattered fracture dissipation is nonnegative for any loading history. For small deviations from the initial state, we propose an elastic potential which permits describing the principal characteristics of the behavior of a saturated porous medium with a brittle skeleton. We study the acoustic properties of the material under study and find their relationship with the strength criterion depending on the accumulated damage and the material current deformation. We consider the problem of scattered fracture of a saturated porous material in a neighborhood of a spherical cavity. We show that the cavity failure occurs if the Hadamard condition is violated.     

脆性材料破坏模拟的网格生成算法

脆性材料的破坏过程具有随机性,当前的网格生成算法没有充分考虑脆性材料破坏时裂纹扩展和碎块生成的随机性。在Persson网格生成算法与Delaunay随机网格剖分理论基础上,提出了一种可根据模拟需要动态控制网格品质的网格生成算法。通过对随机分布点的Delauna三角化,生成初始网格,然后将网格体系比拟为桁架结构,网格节点即为桁架节点。桁架节点在虚拟力作用下可动态调整位置,并最终达到整个体系受力平衡。对Persson 算法中的尺寸分布函数和收敛条件进行了修正,从而提高了收敛速度,并适用于任意形状对象的网格剖分。 基于VC++平台开发了算法程序。通过实例对算法进行了验证,表明算法能够满足脆性材料破碎模拟的需要。     

Effect of microstructure on fracture of brittle materials: Unified approach

A theoretical approach to the fracture of brittle solids based on crack opening displacement and energy rate criterion is presented. The approach allows for the prediction of elastic (Young’s modulus) and fracture (fracture strength and thermal shock) response of a brittle material containing spherical pores and polycrystalline solids containing anisotropic residual stresses.     

Analysis of dynamic stress intensity factors of three-point bend specimen containing crack

A new formula is obtained to calculate dynamic stress intensity factors of the three-point bending specimen containing a single edge crack in this study. Firstly, the weight function for three-point bending specimen containing a single edge crack is derived from a general weight function form and two reference stress intensity factors, the coefficients of the weight function are given. Secondly, the history and distribution of dynamic stresses in uncracked three-point bending specimen are derived based on the vibration theory. Finally, the dynamic stress intensity factors equations for three-pointing specimen with a single edge crack subjected to impact loadings are obtained by the weight function method. The obtained formula is verified by the comparison with the numerical results of the finite element method (FEM). Good agreements have been achieved. The law of dynamic stress intensity factors of the three-point bending specimen under impact loadings varing with crack depths and loading rates is studied.     

Analysis of dynamic stress intensity factors of three-point bend specimen containing crack

A new formula is obtained to calculate dynamic stress intensity factors of the three-point bending specimen containing a single edge crack in this study. Firstly, the weight function for three-point bending specimen containing a single edge crack is derived from a general weight function form and two reference stress intensity factors, the coefficients of the weight function are given. Secondly, the history and distribution of dynamic stresses in uncracked three-point bending specimen are derived based on the vibration theory. Finally, the dynamic stress intensity factors equations for three-pointing specimen with a single edge crack subjected to impact loadings are obtained by the weight function method. The obtained formula is verified by the comparison with the numerical results of the finite element method (FEM). Good agreements have been achieved. The law of dynamic stress intensity factors of the three-point bending specimen under impact loadings varing with crack depths and loading rates is studied.     

3-D numerical simulation of fracture processes in heterogeneous brittle materials

By using the lattice model combined with finite element methods and statistical techniques, a numerical approach is developed to establish mechanical models of three-dimensional heterogeneous brittle materials. A special numerical code is introduced, in which a lattice model and statistical approaches are used to simulate the initial heterogeneity of material properties. The size of displacement-load step is adaptively determined so that only few elements would fail in each load step. When the tensile principal strain in an element exceeds the ultimate strain of this element, the element is considered broken and its Young's modulus is set to be very low. Some important behaviors of heterogeneous brittle materials are indicated using this code. Load-displacement curves and figures of three-dimensional fracture patterns are also numerically obtained, which are similar to those observed in laboratory tests.     

Structural-kinetic stochastic model of fracture and durability of brittle materials

structural-kinetic stochastic approach to the study of the brittle fracture of materials was developed. This approach was used to determine the conditions for passive (latent) and active development of brittle fracture. An asymptotic expression was obtained for the average durability of brittle materials at low stresses at which passive development of fracture occurs.     

Computation of thermal fracture parameters for orthotropic functionally graded materials using Jk-integral

This article introduces a computational method based on the J_k-integral for mixed-mode fracture analysis of orthotropic functionally graded materials (FGMs) that are subjected to thermal stresses. The generalized definition of the J_k-integral is recast into a domain independent form composed of line and area integrals by utilizing the constitutive relations of plane orthotropic thermoelasticity. Implementation of the domain independent J_k-integral is realized through a numerical procedure developed by means of the finite element method. The outlined computational approach enables the evaluation of the modes I and II stress intensity factors, the energy release rate, and the T-stress. The developed technique is validated numerically by considering two different problems, the first of which is the problem of an embedded crack in an orthotropic FGM layer subjected to steady-state thermal stresses; and the second one is that of periodic cracks under transient thermal loading. Comparisons of the mixed-mode stress intensity factors evaluated by the J_k-integral based method to those calculated through the displacement correlation technique (DCT) and to those available in the literature point out that, the proposed form of the J_k-integral possesses the required domain independence and leads to numerical results of high accuracy. Further results are presented to illustrate the influences of the geometric and material constants on the thermal fracture parameters.     

A theory for brittle fracture in compression

A symmetric cylindrical body composed of brittle material, if compressed along its generators may collapse progressively, firstly through catastrophic loss of material adjacent to its lateral surface(s). With increase of the compressive load the reduced cylinder, unable to resist, sunders. The first stage of this type of failure can be explained by the assumed existence of latent interior cracks which open abruptly on a curved, symmetric interior surface when the total energy of the body reaches a critical value determined by the geometry of the initial fracture surface.