A phase-field model for brittle fracture of anisotropic materials

In the present work, a phase field damage model is developed to address the numerical simulation of brittle fracture. This model successfully captures some important aspects of crack propagation, including crack branching and bifurcation. In addition, the proposed phase field model has been developed in the general framework of anisotropic elasticity. It can thus be used for the simulation of brittle fracture in polycrystalline materials, for which crack propagation is impacted by crystallographic orientation because of the anisotropic character of stiffness properties.     

Adaptive isogeometric analysis for phase-field modeling of anisotropic brittle fracture

The surface energy a phase-field approach to brittle fracture in anisotropic materials is also anisotropic and gives rise to second-order gradients in the phase field entering the energy functional. This necessitates C¹ continuity of the basis functions which are used to interpolate the phase field. The basis functions which are employed in isogeometric analysis (IGA), such as nonuniform rational B-splines and T-splines naturally possess a higher order continuity and are therefore ideally suited for phase-field models which are equipped with an anisotropic surface energy. Moreover, the high accuracy of spline discretizations, also relative to their computational demand, significantly reduces the fineness of the required discretization. This holds a fortiori if adaptivity is included. Herein, we present two adaptive refinement schemes in IGA, namely, adaptive local refinement and adaptive hierarchical refinement, for phase-field simulations of anisotropic brittle fracture. The refinement is carried out using a subdivision operator and exploits the Bézier extraction operator. Illustrative examples are included, which show that the method can simulate highly complex crack patterns such as zigzag crack propagation. An excellent agreement is obtained between the solutions from global refinement and adaptive refinement, with a reasonable reduction of the computational effort when using adaptivity.     

An analysis of the conditions of brittle fracture origin

A modified criterion of brittle fracture, a necessary condition of which, the condition of origin of microcracks, is plastic deformation until some value of ₀ dependent upon temperature, is experimentally substantiated. An experimental-calculation method is developed for determination of the relationship of ₀ to temperature T, on the basis of which the ₀(T) relationship is obtained for type 15Kh2MFA steel. It is shown that the proposed formulation of the criterion of brittle fracture makes it possible to consistently describe the fracture processes with different stressed and strained states of the material.Leningrad Branch, Institute of Mechanical Engineering. Translated from Problemy Prochnosti, No. 11, pp. 9–13, November, 1989.     

Crystallography of brittle fracture and deformation twinning in ferritic steels

Abstract

The crystallography of brittle fracture and deformation twinning in ferritic steels is difficult to study experimentally, because of its three-dimensional aspects. The present paper reports the development of methodologies to study the phenomenon via customisation of various electron backscatter diffraction and SEM routes. It is shown that both direct (from the fracture surface) and indirect (from an adjacent polished side) measurements yield valuable information on crystallographic aspects of the fracture processes. Specifically, brittle fracture in three ferritic steels is studied: a C–Mn weld metal, a low alloy Mn–Mo–Ni steel similar to grade A533 and an ultralow carbon (0·002 wt-%C, 0·058 wt-%P) steel plate. The main conclusions resulting from development of the experimental techniques are that cleavage fracture occurs only on {001} planes, and that intergranular accommodation is present at the fracture surface. Further observations suggest that a cleavage side crack, initially deflected by a deformation twin, eventually blunts at the intersection of two deformation twins. This provides a mechanism for limiting the mean length of microcracks during brittle fracture.     

Radiation embrittlement modelling in multi-scale approach to brittle fracture of RPV steels

The purpose of the present article is to develop a multi-scale brittle fracture modelling for irradiated RPV materials. For this development, applicability of local brittle fracture criteria for radiation embrittlement modelling is analysed through comparison of the predicted and test results on radiation embrittlement of RPV steels in terms of ductile-to-brittle transition temperature and fracture toughness. The influence of radiation-induced defects on the processes of cleavage microcrack nucleation and propagation is clarified. The physical-and-mechanical models of the effect of irradiation-induced defects on cleavage microcrack nucleation are developed on the basis of dislocation and brittle fracture theories. Stress-and-strain controlled fracture criterion is developed that allows the adequate prediction of radiation embrittlement by various mechanisms. The differences and commonalities are revealed in the nature of material embrittlement due to cold work and neutron irradiation. The mechanism is explained of significant recovery of fracture resistance properties with simultaneous increase of fraction of intercrystalline fracture after post-irradiation annealing. Engineering approach for prediction of the temperature dependence of fracture toughness as a function of neutron fluence is justified.     

A new method for determining the fracture toughness of main pipeline steels

One of the fundamental aims of fracture mechanics is to define fracture toughness K_IC of a material. Hence, the ASTM E399 standard was developed. However according to the standard, large‐sized specimens are required to determine the fracture toughness of low alloy carbon steels. ASTM E1921 standard was developed on the fracture toughness of ferritic steels. In this study, a new method was proposed to determine the fracture toughness of ferritic steels. The purpose of the present paper is to compare the results of the method with the experimental results. Two steels that are used in gas and oil main pipelines were investigated in this study.     

Influence of the modes of thermomechanical preloading on the resistance of heat-resistant steels to brittle fracture

We describe the methods and results of the experimental investigation of the influence of various modes of thermomechanical preloading on the resistance of nuclear pressure-vessel steels to brittle fracture. We studied specimens of different thickness (25–150 mm) made of the base and weld metals of the vessels of water-moderated, water-cooled nuclear power reactors. The materials under consideration belong to different strength classes. It is shown that the positive effect of thermomechanical preloading is preserved or even strengthened after the subcritical ductile growth of a crack in the process of preloading. We compare the available experimental data with the results of numerical calculations performed by using the Chell model. It is shown that the Chell model fails to explain some experimental data. Institute for Problems of Strength, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 2, pp. 126–138, March–April, 1999.     

Micromechanical modeling of grain boundary resistance to cleavage crack propagation in ferritic steels

In ferritic steels a propagating cleavage microcrack changes its propagation direction as it advances from grain to grain. This is due to differences in the orientation of the cleavage planes of two neighboring grains. In order to reach a cleavage plane in a new grain, a microcrack must first penetrate the grain boundary. Grain boundaries therefore act as natural barriers in cleavage fracture. The influence of a grain boundary and the associated misorientation in cleavage planes on crack arrest is here examined using a 3D finite element model with axisymmetric periodicity, representing two grains whose cleavage planes are tilted and twisted relative to each other. The temperature dependent mechanical properties of ferrite are modeled using a temperature dependent viscoplastic response. The development of the crack front as the microcrack penetrates through a grain boundary is here presented. The influence of the twist misorientation on the critical grain size, defined as the largest grain size that can arrest a rapidly propagating microcrack, is examined in a temperature range corresponding to the ductile to brittle transition (DBT) region. It is shown that when both tilt and twist misorientation are present, the influence of tilt and twist, respectively, on crack growth resistance can be decoupled.