Effect of triaxial stress constraint on the deformation and fracture of polymers

One purpose of this paper is to give a brief overview on the research status of deformation, fracture and toughening mechanisms of polymers, including experimental, theoretical and numerical studies. Emphasis is on the more recent progresses of micromechanics of rubber particle cavitation and crazing, and the development of fracture criteria for ductile polymers. The other purpose is to study the effect of triaxial stress constraint on the deformation and fracture behavior of polymers. Polycarbonate (PC), acrylonitrile-butadienestyrene (ABS) and PC/ABS alloy are considered in this investigation. A series of circumferentially blunt-notched bars are used to experimentally generate different triaxial stress fields. The fracture surfaces of specimens with different notch radius are examined by scanning electron microscope (SEM) to study the fracture and toughening mechanisms of polymer alloy. It is shown that the triaxial stress constraint has a significant effect on the deformation, fracture and toughening of PC, ABS and PC/ABS alloy. We will also discuss the extent to which a micromechanics criterion proposed by the first author can serve as a fracture criterion for ductile polymers. A new ductile fracture parameter is emphasized, which can be employed to evaluate the fracture ductility of polymers. Stress state independence of the parameter for the PC, ABS and PC/ABS alloy has been experimentally verified. The project supported by the National Natural Science Foundation of China (10125212), the Trans-Century Training Program Foundation and the Key Research Fund of the Education Ministry of China (01159)     

Mesoscopic modeling of Acoustic Emission through an energetic approach

The aim of the present work is to present a simple model for damage progression and Acoustic Emission that correctly accounts for energy dissipation due to the formation of micro-cracks and the creation of surfaces in a material undergoing external loading, and thus to derive the scaling behaviour observed in experiments. To do this, energy balance considerations are included in a Fibre Bundle Model approach. The model predictions are first illustrated in a uniaxial test under quasistatic loading conditions. Numerical results are then compared to experimental data relative to tests on masonry elements of various sizes subjected compression. The scaling properties of Acoustic Emission under the chosen energy balance assumptions is analyzed and compared to previous numerical and experimental results in the literature. Power-law scaling behaviour is found with respect to specimen dimensions.     

A study of the generation and creep relaxation of triaxial residual stresses in stainless steel

This paper presents results from a numerical and experimental research programme motivated by the need to predict creep damage generated by multi-axial states of stress in austenitic stainless steels. It has been hypothesized that highly triaxial residual stress fields may be sufficient to promote creep damage in thermally aged components, even in the absence of in-service loads. Two prerequisites to test this hypothesis are the provision of test specimens containing a highly triaxial residual stress field and an accurate knowledge of how this residual stress field relaxes due to creep. Creep damage predictions may then be made for these specimens and compared to damage observed in experiments. This paper provides solutions to both of these prerequisites. Cylindrical and spherical test specimens made from type 316H stainless steel are heated to 850 °C and then quenched in water. Finite element predictions of the residual stress state, validated by extensive neutron diffraction measurements, are presented which confirm the high level of triaxiality present in the specimens. The specimens are then thermally aged at 550 °C and numerical predictions of the residual stress relaxation are given, again validated by extensive neutron diffraction measurements. The results confirm the validity of the creep relaxation models employed. In addition, the results show the influence of specimen size and permit comparisons to be made between three different types of neutron diffractometers.     

近场动力学研究进展与岩石破裂过程模拟

近场动力学（Peridynamics,PD）作为一种新兴的非局部性理论,在非连续处不需要任何处理,能够很好表述模型从连续到非连续的过程。首先,在PD基本理论简介的基础上,系统回顾了PD的国内外研究现状。其次,采用键型PD理论对非均匀性的圆孔岩板单轴拉伸破裂过程进行了二维数值模拟,采用态型PD理论对单轴、常规三轴以及真三轴等不同压缩条件下的岩石破裂过程进行了三维数值模拟,并以加拿大Mine-by隧洞为例对现场岩体破裂过程进行了模拟,结果表明PD在岩石破裂过程模拟上具有较强适用性。最后,指出当前PD在岩石破裂过程模拟中存在的主要问题和未来值得开展的若干研究课题。     

Damage constitutive for high strength concrete in triaxial cyclic compression

A constitutive relationship for high strength concrete in triaxial monotonic and cyclic compressions is developed based on the continuum damage mechanics. The bounding surface concept is employed in the formulation of the theoretical model. An experimental program was undertaken in order to establish databases for high strength concrete under triaxial monotonic and cyclic compressions. The stress-strain responses of high strength concrete subjected to triaxial monotonic and cyclic compressions were acquired through an experimental program. Comparison of the stress strain results indicates good agreement between the theoretical model and the experimental data.     

Homogenized rigid-plastic model for masonry walls subjected to impact

A simple rigid-plastic homogenization model for the analysis of masonry structures subjected to out-of-plane impact loads is presented. The objective is to propose a model characterized by a few material parameters, numerically inexpensive and very stable. Bricks and mortar joints are assumed rigid perfectly plastic and obeying an associated flow rule. In order to take into account the effect of brickwork texture, out-of-plane anisotropic masonry failure surfaces are obtained by means of a limit analysis approach, in which the unit cell is sub-divided into a fixed number of sub-domains and layers along the thickness. A polynomial representation of micro-stress tensor components is utilized inside each sub-domain, assuring both stress tensor admissibility on a regular grid of points and continuity of the stress vector at the interfaces between contiguous sub-domains. Limited strength (frictional failure with compressive cap and tension cut-off) of brick-mortar interfaces is also considered in the model, thus allowing the reproduction of elementary cell failures due to the possible insufficient resistance of the bond between units and joints.Triangular Kirchhoff-Love elements with linear interpolation of the displacement field and constant moment within each element are used at a structural level. In this framework, a simple quadratic programming problem is obtained to analyze entire walls subjected to impacts.In order to test the capabilities of the approach proposed, two examples of technical interest are discussed, namely a running bond masonry wall constrained at three edges and subjected to a point impact load and a masonry square plate constrained at four edges and subjected to a distributed dynamic pressure simulating an air-blast. Only for the first example, numerical and experimental data are available, whereas for the second example insufficient information is at disposal from the literature. Comparisons with standard elastic–plastic procedures conducted by means of commercial FE codes are also provided. Despite the obvious approximations and limitations connected to the utilization of a rigid-plastic model for masonry, the approach proposed seems able to provide results in agreement with alternative expensive numerical elasto-plastic approaches, but requiring only negligible processing time. Therefore, the proposed simple tool can be used (in addition to more sophisticated but expensive non-linear procedures) by practitioners to have a fast estimation of masonry behavior subjected to impact.     

Identification of the representative crack length evolution in a multi-level interface model for quasi-brittle masonry

It is proposed here to identify the law of crack length evolution with a small number of parameters governing a recently presented model (Rekik and Lebon, submitted for publication) describing the interface behavior in damaged masonry. Studies on non-confined medium- and large-sized masonry structures have shown that it is necessary to obtain a linear increasing crack in the post-peak part of the “stress–strain or –displacement” diagram. In confined masonry structures showing softening and sliding parts, the results obtained with this crack evolution failed to match the experimental data. The crack lengths identified in the post-peak part at several points on the experimental “stress–displacement” diagram show that the representative crack length is a bilinear or trilinear function describing the increase in the crack length with respect to the decrease in the shear stress. Numerical studies on medium- and large-sized masonry structures consisting of the same materials subjected to various loads were performed to determine the ultimate crack length, and the results are relatively insensitive to the size of the masonry and the type of the load applied. The numerical local fields determined in the elementary and full-scale structures investigated were used to test the validity of the present model at the local scale, as well as to obtain an additional unilateral condition in the case of compressed masonry structures in order to prevent overlapping between the masonry components.     

燃气爆炸作用下蒸压加气混凝土砌体墙的加固性能

为研究燃气爆炸作用下蒸压加气混凝土砌体墙的加固性能,基于有限元软件LS-DYNA,建立了砌体墙简化数值模型,分析了GB 50779-2012 石油化工控制室抗爆设计规范中建议的荷载作用下砌体墙高度和厚度的影响,对比了玄武岩纤维(basalt fiber reinforced plastic, BFRP)布与喷涂式聚脲对蒸压加气混凝土单向砌体墙的加固效果,并以防止砌体墙倒塌为设计目标,给出了加固建议。研究表明,本文中建立的简化数值模型能较好地模拟燃气爆炸作用下蒸压加气混凝土砌体墙的变形和破坏模式,计算结果与试验吻合良好;《规范》建议荷载作用下,未加固砌体墙以弯曲破坏为主,随着墙体高度增加,破坏模式由弯曲破坏向剪切破坏转变;BFRP布条加固可以有效提高墙体抗弯刚度和压拱效应,而聚脲涂层加固对抗弯刚度提高有限但墙体拉拱效应明显,二者均能显著提高墙体抗爆性能;加固墙体均发生弯曲破坏,BFRP布条材料的断裂一般发生在墙体位移最大处,而聚脲涂层材料的断裂发生在跨端边界处。     

氯盐腐蚀对充填膏体蠕变特性影响的试验研究

为探索充填膏体在经过不同时长氯盐腐蚀后的蠕变规律,采用饱和氯化钠(NaCl)溶液,对养护28天的充填膏体进行干湿循环加速腐蚀试验。采用TAW2000型岩石三轴试验机,将未经腐蚀的试件和经过不同时间腐蚀的试件分别进行不同应力水平的三轴蠕变试验,并对试验结果进行对比分析。在试验基础上,建立了氯盐腐蚀条件下充填膏体的蠕变模型。将一个应变触发的非线性粘壶串联在原来的Poynting-Thomson模型上,建立了一个改进Poynting-Thomson模型。研究表明:在腐蚀早期,经过腐蚀的充填膏体蠕变变形较之未经腐蚀的小;随着腐蚀时间延长,充填膏体的蠕变变形逐渐增大;在长时间腐蚀、高应力水平同时存在的条件下,充填膏体会出现加速蠕变现象。本文建立的蠕变模型与蠕变试验数据吻合较好,能够反映出充填膏体在氯盐腐蚀作用下的蠕变特征。     

A failure criterion for fiber reinforced polymer composites under combined compression–torsion loading

A fracture mechanics based failure criterion for unidirectional composites under combined loading has been developed. The predictions from this criterion have been compared with experimental data obtained from combined compression–torsion loading of glass and carbon fiber reinforced polymer composites of 50% fiber volume fraction. The specimens were loaded under rotation control and displacement control in a proportional manner. Comparison of the Budiansky–Fleck kinking model, specialized to a solid circular cylinder, and the new failure model against experimental data suggests that the Budiansky–Fleck model predictions do not capture the variation of compressive strength as a function of shear stress for glass fiber composites. This is because these composites fail predominantly by compressive splitting. The Budiansky–Fleck model predictions are appropriate for composites that fail by compressive kinking. The new model predictions capture the experimental results for glass composites where the compression strength is initially unaffected by shear stress but undergoes a drastic reduction when a critical value of shear stress is reached.     

Magnetoelastic fracture of soft ferromagnetic materials

Effects of magnetic field on fracture toughness of soft ferromagnetic materials were studied using experimental techniques and theoretical models. The manganese–zinc ferrite with a single-edge-notch-beam (SENB) were chosen to be the specimen and the Vickers’ indentation specimen subjected to a magnetic field were chosen to be the specimens. Results indicate that there is no significant variations of the measured fracture toughness of the manganese–zinc ferrite ceramic in the presence of the magnetic field. The theoretical model involves an anti-plane shear crack with finite length in an infinite magnetostrictive body where an in-plane magnetic field prevails at infinity. Magnetoelasticity is used. The crack-tip elastic field is different from that of the classical mode III fracture problem. Furthermore, the magnetoelastic fracture of the soft ferromagnetic material was studied by solving the stress field for a soft ferromagnetic plane with a center-through elliptical crack. The stress field at the tip of a slender elliptical crack is obtained for which only external magnetic field normal to the major axis of the ellipse is applied at infinity. The results indicate that the near field stresses are governed by the magnetostriction and permeability of the soft ferromagnetic material. The induction magnetostrictive modulus is a key parameter for finding whether magnetostriction or magnetic-force-induced deformation is dominant near the front an elliptically-shaped crack. The influence of the magnetic field on the apparent toughness of a soft ferromagnetic material with a crack-like flaw can be regarded approximately in two ways: one possesses a large induction magnetostrictive modulus and the other has a small modulus. Finally, a small-scale magnetic-yielding model was developed on the basis of linear magnetization to interpret the experimental results related to the fracture of the manganese–zinc ferrite ceramics under magnetic field. Studied also is the fracture test of the soft ferromagnetic steel with compact tension specimens published in the existing literature.     

Plasticity and fracture of martensitic boron steel under plane stress conditions

Two series of multiaxial experiments are performed to characterize the mechanical behavior of a hot formed martensitic 22MnB5 boron steel. In the first series, flat specimens of uniform cross-section are subjected to various combinations of tensile and shear loading to characterize the elasto-plastic response. Butterfly-shaped specimens of non-uniform cross-section are used for the second series to study the onset of fracture in the martensitic steel. It is found from the analysis of the experimental results that the planar isotropic Hill’48 yield function along with an associated flow rule provides good estimates of the stress–strain response over a wide range of loading paths. The fracture experiments demonstrate that the crack initiation depends strongly on the loading state. A simple stress triaxiality dependent phenomenological fracture model is calibrated to describe the onset of fracture. Using the proposed plasticity and fracture model, numerical simulations of the fracture of tensile specimens of different notch radii are performed and compared with experiments.     

Effect of Moisture Movement on Tested Thermal Conductivity of Moist Aerated Autoclaved Concrete

The purpose of this work was to study both theoretically and experimentally the process of moisture redistribution and heat transfer due to phase changes during the tests of thermal conductivity in aerated autoclaved concrete (AAC) moist specimens. The different moisture contents of the test samples were obtained in climatic chamber at equilibrium conditions reached with constant air temperature and variable relative humidity. The moist specimens were sealed inside highly impermeable polyethylene bag, as required by UNI 10051, and placed in a heat flow meter apparatus. During the experimental thermal conductivity measurements, the temperature and heat flow rate were measured under transient and steady state conditions. A theoretical analysis of the heat and mass transfer process was performed and then a suitable numerical model was used to predict the moisture redistribution and heat transfer due to the phase changes. The theoretical model has been compared against the experimental data. Substantial agreement between numerical results and experimental data was found. Then several numerical simulations have been performed to study the influence of the errors due to phase changes and non-uniform moisture distribution during the test of thermal conductivity of moist AAC specimens.     

微薄梁三点弯曲的尺度效应研究

应用高灵敏度的力传感器以及时间序列电子散斑干涉法，同时测出了不同厚度纯镍薄片三点 弯曲试件的抗力与变形，得到薄梁中心点处的载荷与挠度曲线. 应用Fleck和Hutchinson 的偶应力理论，结合平面应变弯曲模型，建立了薄梁处于弹性状态和弹塑性状态的 控制方程, 应用Runge-Kutta法进行数值求解，并将计算得到的载荷-挠度曲线以及无量纲化弯矩-表面 应变曲线和实验结果进行了比较. 在理论计算过程中，没有拟合任何材料参数，所有的材料 参数均来自实验测量的结果，材料特征尺度也是根据Stolken和Evans的工作给出 的. 结果表明: 应用偶应力理论预测的结果和实验结果符合良好，而经典理论的预测结果与 实验不相符合.     

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.     

应力三轴度的有限元计算修正

对某高强度钢制成的光滑圆棒和缺口圆棒进行了系列准静态拉伸实验,采用ABAQUS对每个试 件进行了数值模拟,得到了该材料的真实应力应变曲线,拟合出了J-C本构模型和失效模型的部分材料常数。 最后,对该高强度钢制成的平板进行了撞击实验,并用得到的J-C模型对平板撞击实验进行了数值模拟,计算 结果与实验结果吻合很好,证明利用数值模拟并修正应力三轴度的方法是可行的。     

On indentation and initiation of fracture in glass

The influence of indenter elasticity on Hertzian fracture initiation at frictional dissimilar elastic contact has been examined experimentally and numerically. In flat float glass specimens initiation of cone cracks has been observed and fracture loads measured with steel and tungsten carbide indenters at monotonically increasing loading and during a load cycle. The observed effect of indenter elasticity on fracture loads was found to be qualitatively different from the one predicted by the Hertz contact theory. This discrepancy may be explained by the presence of interfacial friction. The friction coefficient between the indenters and the specimen was measured and a contact cycle at finite Coulomb friction has been analyzed numerically. The influence of the indenter elasticity and the friction coefficient on the surface maximum tensile stress has been investigated and the results concerning the influence of these parameters on the fracture loads as given based on a critical stress fracture criterion. The obtained computational results were found to be in better agreement with experimental findings as compared to the predictions based on the frictionless contact theory. A remaining quantitative discrepancy was attributed to the well-known fact that a Hertzian macro-crack initiates from pre-existing defects on the specimen’s surface. In order to account for the influence of the random distribution of these defects a Weibull statistics was introduced. The predicted critical loads corresponding to the 50% failure probability were found to be in close agreement with experimentally observed ones.     

Constitutive modeling of aluminum foam including fracture and statistical variation of density

An existing constitutive model applicable for aluminum foam was evaluated. The model was implemented in LS-DYNA, and several test cases were analyzed and compared to experimental data. The numerical analyses consisted of foam subjected to both simple and more complex loading conditions where fracture was of varying importance. Therefore, simple fracture criteria were added to the model. Additionally, the inhomogeneities in the foam were modeled by incorporating the possibility of statistical variation of the foam density. The implemented model is efficient and robust, and gives satisfactory results compared with the experimental results.     

An elasto-plastic model for granular materials with microstructural consideration

In this paper, we have extended the granular mechanics approach to derive an elasto-plastic stress–strain relationship. The deformation of a representative volume of the material is generated by mobilizing particle contacts in all orientations. Thus, the stress–strain relationship can be derived as an average of the mobilization behavior of these local contact planes. The local behavior is assumed to follow a Hertz–Mindlin’s elastic law and a Mohr–Coulomb’s plastic law. Essential features such as continuous displacement field, inter-particle stiffness, and fabric tensor are discussed. The predictions of the derived stress–strain model are compared to experimental results for sand under both drained and undrained triaxial loading conditions. The comparisons demonstrate the ability of this model to reproduce accurately the overall mechanical behavior of granular media and to account for the influence of key parameters such as void ratio and mean stress. A part of this paper is devoted to the study of anisotropic specimens loaded in different directions, which shows the model capability of considering the influence of inherent anisotropy on the stress–strain response under a drained triaxial loading condition.