A model for brittle fracture based on the hybrid phase field model

We propose a phase field model for crack propagation based on the hybrid model and justify the model by constructing a family of asymptotic solutions.     

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。     

A 3-D ellipsoidal flaw model for brittle fracture in compression

Engineering materials are rarely free of flaws. Mode I cracking from pre-existing flaws is the major cause of the brittle fracture in compression of materials such as concrete and rock. A 3-D ellipsoidal flaw model is used to show the significant influence of flaw geometry on crack initiation in uniform uniaxial, biaxial and triaxial compression. The model shows that the governing criterion for crack initiation may change from energy to stress with increasing crack size, and that for voids of similar size a spherical void is the most critical shape for crack initiation. The model thus provides a basis for a better understanding of both the phenomenon and the mechanism of brittle fracture in compression.     

Sharp-crack limit of a phase-field model for brittle fracture

A matched asymptotic analysis is used to establish the correspondence between an appropriately scaled version of the governing equations of a phase-field model for fracture and the equations of the two-dimensional sharp-crack theory of Gurtin and Podio-Guidugli (1996) that arise on assuming that the bulk constitutive behavior is nonlinearly elastic, requiring that surface energy provides the only factor limiting crack propagation, and assuming that the fracture kinetics are isotropic. Consistent with the prominence of the configurational momentum balance at the crack tip in the latter theory, the approach capitalizes on the configurational momentum balance that arises naturally in the context of the phase-field model. The model developed and utilized here incorporates irreversibility of the phase-field evolution. This is achieved by introducing a suitable constraint and by carefully heeding the influence of that constraint on the kinetics underlying microstructural changes associated with fracture. The analysis is predicated on the assumption that the phase-field variable takes values in the closed interval between zero and unity.     

A nonlocal theory for brittle fracture

In this paper, a nonlocal theory of fracture for brittle materials has been systematically developed, which is composed of the nonlocal elastic stress fields of Griffith cracks of mode-I, II and III, the asymptotic forms of the stress fields at the neighborhood of the crack tips, and the maximum tensile stress criterion for brittle fracture. As an application of the theory, the fracture criteria of cracks of mode-I, II, III and mixed mode I–II, I–III are given in detail and compared with some experimental data and the theoretical results of minimum strain energy density factor.     

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.     

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.     

Crack front penetration in transgranular cleavage cracking in an iron-silicon alloy

Based on the analysis of the crack trapping effect of cleavage ridges and penetration of crack front segments in an iron-silicon alloy, the distance between break-through points along a high-angle grain boundary is investigated. If the break-through points are close to each other, the crack trapping effect is dominant; otherwise, the grain boundary separation in break-through windows governs the front transmission process. The relationship between the overall grain boundary fracture resistance and the break-through-point distance is quite complex. The minimum grain boundary resistance is achieved when the break-through points are about 2–3 μm apart, which is also influenced by the grain boundary shear strength, the crystallographic toughness and orientation, as well as the crack front profile.     

一个考虑形变能影响的脆断强度条件

针对常用强度理论解决复杂应力状态生断裂存在的问题，分析了由形状改变比能引起的塑性变形对脆断的影响，给出了一个新的脆断强度条件，并通过铸铁破坏试验作了验证。     

A statistical, physical-based, micro-mechanical model of hydrogen-induced intergranular fracture in steel

Intergranular cracking associated with hydrogen embrittlement represents a particularly severe degradation mechanism in metallic structures which can lead to sudden and unexpected catastrophic fractures. As a basis for a strategy for the prognosis of such failures, here we present a comprehensive physical-based statistical micro-mechanical model of such embrittlement which we use to quantitatively predict the degradation in fracture strength of a high-strength steel with increasing hydrogen concentration, with the predictions verified by experiment. The mechanistic role of dissolved hydrogen is identified by the transition to a locally stress-controlled fracture, which is modeled as being initiated by a dislocation pile-up against a grain-boundary carbide which in turn leads to interface decohesion and intergranular fracture. Akin to cleavage fracture in steel, the “strength” of these carbides is modeled using weakest-link statistics. We associate the dominant role of hydrogen with trapping at dislocations; this trapped hydrogen reduces the stress that impedes dislocation motion and also lowers the reversible work of decohesion at the tip of dislocation pile-up at the carbide/matrix interface. Mechanistically, the model advocates the synergistic action of both the hydrogen-enhanced local plasticity and decohesion mechanisms in dictating failure.     

Uniqueness in brittle fracture mechanics

It is shown that the boundary initial value problem of brittle fracture mechanics has, at most, one solution in the class of all vector fields having finite energy at each instant. No definite assumption on the elasticity tensor is made.     

Coarse-graining atomistic dynamics of brittle fracture by finite element method

In this work we present the finite element (FE) implementation of an atomistic formulation of balance equations and its application to coarse-grained (CG) simulation of dynamic fracture. First, we simulate a notched specimen that contains about 1.8 million atoms by the CG-FE method, and we compare the CG-FE results with that by all-atom molecular dynamics (MD) simulations. We find that CG-FE simulations with about 5% degrees of freedom of the MD simulation can capture the essential dynamic features, not in exact correspondence, but qualitatively and quantitatively similar to that obtained by MD simulations. We then proceed to simulate a series of micron-sized specimens by the CF-FE method. We find that it is the interaction of the forward propagating crack with the stress waves being reflected back by the boundaries of the specimen that triggers the dynamic instability and hence the branching of cracks in micron-sized specimens. The potential application of the method and future work for improvements are discussed.     

On possible causes of brittle fracture

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 137–141, May–June, 1988.     

弹塑性体脆断相场模型的一致性无单元伽辽金法

采用无单元伽辽金法（EFG）对弹塑性体脆性断裂的相场模型进行了数值实现。利用无单元法便于构建高阶近似函数的优势,位移和相场均采用二阶移动最小二乘（MLS）近似。刚度阵的数值积分采用更为高效的二阶一致三点积分格式QC3（Quadratically Consistent 3-point integration scheme）。本构算法采用Newton-Raphson迭代和弹塑性一致性切线模量。数值结果表明了本文方法模拟弹塑性体脆性断裂的有效性。     

Kinematic features of the brittle fracture phenomenon

Summary Normal-fracture surfaces of various high-polymers were investigated with the aid of light microscopy. The common fracture pattern is discussed in relation with the kinematic fracture picture introduced bySmekal (1–3). Attention is paid to radial traces and hyperbolic traces, as well as to other morphological features. With the aid of the morphological picture and results of mechanical surface roughness measurements, the three-dimensional density (volume population) of fracture sources could, at polymethylmethacrylate, be roughly estimated. The geometry of fracture sources of polymethylmethacrylate was elucidated by means of electron microscopy. Supplementary experiments performated at normal-fracture surfaces of polymethylmethacrylate showed the effect of a 90°-rotation of the largest principal stress upon the critical condition of inhomogeneities.

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Zusammenfassung Bruchflächen verschiedener Hochpolymeren wurden lichtmikroskopisch untersucht. Die Bruchfiguren werden an Hand des kinematischen Bildes des Bruchvorgangs, wie esSmekal entwickelte, betrachtet. Besondere Aufmerksamkeit wurde den radialen und hyperbolischen Spuren sowie den anderen morphologischen Zügen gewidmet. Mit Hilfe des morphologischen Bildes und der Ergebnisse von mechanischen Messungen der Oberflächenrauhigkeit konnte grob für Polymethylmethacrylat die 3-dimensionale Dichte (Volumenhäufigkeit) der Quellen für den Bruch abgeschätzt werden. Die geometrische Form der Bruchquellen für Polymethylmethacrylat wurde elektronenmikroskopisch geklärt. Ergänzende Experimente an Normal-Bruchflächen von Polymethylmethacrylat zeigen den Effekt einer 90°-Drehung der größten Hauptspannung auf die kritische Inhomogenitätsbedingung.

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Presented at the conference Flow, Fatigue and Failure held in Leeds on January 8th and 9th, 1959, by the British Society of Rheology.     

A new damage model for microcrack-weakened brittle solids

In the present paper, a micromechanically based damage model for microcrack-weakened solids is developed. The concept of the domain of microcrack growth (DMG) is defined and used to describe the damage state and the anisotropic properties of brittle materials. After choosing an appropriate fracture criterion of microcrack, we obtain the analytical expression of DMG under a monotonically increasing proportional plane stress. Under a complex loading path, the evolution equation of DMG and the overall effective compliance tensor of damaged materials are given. The project supported by National Natural Science Foundation of China     

The mixed mode brittle fracture criteria in siliding mode fracture

It is well-known that the present mixed mode brittle fracture criteria are all theopening mode fracture criterion.We consider that mixed mode brittle fracture of slidingmode fracture exists too.Hence we propose three criteria of mixed mode brittle fracture ofsliding mode fracture;:the radial shearing stress criterion,the maximum shearing stresscriterion and the distortional strain-energy-density criterion.Thus,we can overall explainthe phenomena of brittle fracture in the structural elements with cracks.     

Phase-field models for brittle and cohesive fracture

In this paper we first recapitulate some basic notions of brittle and cohesive fracture models, as well as the phase-field approximation to fracture. Next, a critical assessment is made of the sensitivity of the phase-field approach to brittle fracture, in particular the degradation function, and the use of monolithic versus partitioned solution schemes. The last part of the paper makes extensions to a recently developed phase-field model for cohesive fracture, in particular for propagating cracks. Using some simple examples the current state of the cohesive phase-field model is shown.     

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.