Microplane damage model for fatigue of quasibrittle materials: Sub-critical crack growth,lifetime and residual strength

In contrast to metals and fine grained ceramics, fatigue in concrete and other quasibrittle materials occurs in a large fracture process zone that is not negligible compared to the structure size. This causes the fatigue to be combined with triaxial softening damage whose localization is governed by a finite material characteristic length. A realistic model applicable to both has apparently not yet been developed and is the goal of this paper. Microplane model M7, shown previously to capture well the nonlinear triaxial behavior of concrete under a great variety of loadings paths, is extended by incorporating a new law for hysteresis and fatigue degradation, which is formulated as a function of the length of the path of the inelastic volumetric strain in the strain space. The crack band model, whose band width represents a material characteristic length preventing spurious localization, is used to simulate propagation of the fatigue fracture process zone. Thus the fatigue crack with its wide and long process zone is simulated as a damage band of a finite width. For constant amplitude cycles, the model is shown to reproduce well, up to several thousands of cycles, the Paris law behavior with a high exponent previously identified for concrete and ceramics, but with a crack growth rate depending on the structure size. Good agreement with the crack growth histories and lifetimes previously measured on three-point bend beams of normal and high strength concretes is demonstrated. The calculated compliance evolution of the specimens also matches the previous experiments. The model can be applied to load cycles of varying amplitude, to residual strength under sudden overload and damage under nonproportional strain tensor variation. Application to size effect in fatigue is relegated to a follow-up paper, while a cycle-jump algorithm for extrapolation high-cycle fatigue with millions of cycles remains to be researched.     

Scaling of quasibrittle fracture: hypotheses of invasive and lacunar fractality, their critique and Weibull connection

Considerable progress has been achieved in fractal characterization of the properties of crack surfaces in quasibrittle materials such as concrete, rock, ice, ceramics and composites. Recently, fractality of cracks or microcracks was proposed as the explanation of the observed size effect on the nominal strength of structures. This explanation, though, has rested merely on intuitive analogy and geometric reasoning, and did not take into account the mechanics of crack propagation. In this paper, the energy-based asymptotic analysis of scaling presented in the preceding companion paper in this issue [1] is extended to the effect of fractality on scaling. First, attention is focused on the propagation of fractal crack curves (invasive fractals). The modifications of the scaling law caused by crack fractality are derived, both for quasibrittle failures after large stable crack growth and for failures at the initiation of a fractal crack in the boundary layer near the surface. Second, attention is focused on discrete fractal distribution of microcracks (lacunar fractals), which is shown to lead to an analogy with Weibull's statistical theory of size effect due to material strength randomness. The predictions ensuing from the fractal hypothesis, either invasive or lacunar, disagree with the experimentally confirmed asymptotic characteristics of the size effect in quasibrittle structures. It is also pointed out that considering the crack curve as a self-similar fractal conflicts with kinematics. This can be remedied by considering the crack to be an affine fractal. It is concluded that the fractal characteristics of either the fracture surface or the microcracking at the fracture front cannot have a significant influence on the law of scaling of failure loads, although they can affect the fracture characteristics. Walter P. Murphy, Professor| of This revised version was published online in July 2006 with corrections to the Cover Date.     

A fatigue life prediction method for coke drum base,weld, and HAZ materials from tensile properties

The importance of material fatigue information in design has been well recognized. There are a few existing fatigue life prediction methods based on materials tensile properties. Some of these fatigue life prediction methods can be successfully applied for non-heat affected materials. However, industrial components, such as pressure vessel and pipelines are commonly constructed by welding parts together. The fatigue lives of welded section and its surrounding material could be greatly affected by the welding process. Therefore, it is beneficial to develop a fatigue life prediction model for the weld and surrounding heat affected zone (HAZ) materials based on their tensile testing data. In this paper, fatigue lives of base material and its weld and HAZ materials for constructing coke drums are studied. Mechanical properties are first obtained from the tensile tests. Then, fully-reversed strain-controlled fatigue tests were performed. It is found that the fatigue life of pure base material is roughly twice of the weld and four time of the HAZ at the same strain amplitude. Four-point correlation (FPC) method by Manson can reasonably predict the life of base material. However, it over-predicts the lives of weld and HAZ. By introducing two reduction factors R_plastic and R_elastic for the weld and HAZ material respectively into the FPC method, the over-prediction can be rectified. Therefore, the proposed modified FPC method could be applied in predicting fatigue lives of weld and HAZ materials.     

无序材料微裂缝分形几何与尺寸效应的微观机理

针对一些含有相同的微裂缝随机分布概率密度但无序度不同的材料,建立了模拟材料断裂力学行为的二维不连续位移法边界元数值计算模型,实现了材料微裂缝的生长、扩展到最终破坏的全过程数值模拟.从分形几何的新视角深入地揭示了脆性或准脆性无序材料产生尺寸效应的微观机理.材料断裂力学行为的数值模拟结果与Bazant尺寸效应定律相符,不仅与微缺陷的密度有关,更与微缺陷大小随机分布的无序度相关,无序度越大的材料其尺寸效应越明显.得到了用初始分形维数D0表示的关于材料断裂强度的分形维数Dσ经验公式,可以更深入地解释材料的微观尺寸效应机理和断裂过程.     

Development of semi-empirical formulation for extracting materials properties from nanoindentation measurements: Residual stresses, substrate effect, and creep

Nanoindentation is one of the most popular techniques for characterizing the mechanical properties of micro- or nano-structured metals or dielectric thin films. However, the obtained experimental data can only provide the relationship between the applied load and the penetration depth. Mechanics models are therefore required to convert the test data into the corresponding material properties. In this work, the effect of residual stress, the substrate effect, and the creep of materials subjected to the indentation test are discussed in order to establish appropriate conversion formulas or criteria for extracting the interested material properties. Dimensional analyses are firstly performed to find the governing parameters and to obtain scaling relationships for subsequent finite element analysis. With the described procedure, models have been developed to convert nanoindentation test data into the desired material properties. Those models provide useful tools for extracting specific material properties, such as residual stress, creep exponent, and stress relaxation time constant. Specifically, this investigation also shows that for the situation of soft film/hard substrate combination, the indentation behavior is essentially identical if the modulus of the substrate is 10 times higher than that of the corresponding film and the response deviates consistently from that of bulk material with increasing of indentation depth. For penetration depth less than 10% of the film thickness, the deviation could be acceptable. On the other hand, significant deviation is observed for hard film/soft substrate systems. In summary, by integrating the models proposed by this work and data from standard tests, it is possible to obtain the Young's modulus, hardness, and the viscoelastic properties as well as the residual stress for a specific material through indentation characterization.     

Simplified model for the fatigue growth analysis of surface cracks in round bars under mode I

The fatigue growth of an edge flaw in a round bar under cyclic tension or bending loading is examined, using a two-parameter numerical model. First, it is shown that the crack front evolution is defined by a very small number of parameters, which varies during crack growth. Approximated solutions for both the crack propagation path and the stress intensity factor are derived, and the fatigue predictions using this simple analytical method are finally compared with the numerical results.     

Cohesive Crack Model with Rate-Dependent Opening and Viscoelasticity: II. Numerical Algorithm, Behavior and Size Effect

In the preceding companion paper (Bažant and Li, 1995), the solution of an aging viscoelastic law was structure containing a cohesive crack with a rate-dependent stress-displacement softening law was reduced to a system of one-dimensional integro-differential equations involving compliance functions for points on the crack faces and the load point. An effective numerical algorithm for solving these equations, which dramatically reduces the computer time compared to the general two-dimensional finite element solution, is presented. The behavior of the model for various loading conditions is studied. It is shown that the model can closely reproduce the available experimental data from fracture tests with different loading rates spanning several orders of magnitude, and tests with sudden changes of the loading rate. Influence of the loading rate on the size effect and brittleness is also analyzed and is shown to agree with experiments. This revised version was published online in July 2006 with corrections to the Cover Date.