A model for the static fracture toughness of ductile structural steel

Fracture of ductile structural steels generally occurs after void initiation, void growth and void coalescence. In order for ductile fracture of structural steels to occur, energy must be spent to induce void initiation and void growth. Therefore, fracture toughness for ductile fracture should be contributed from void initiation and void growth. On the basis of this suggestion static fracture toughness (K_IC) of ductile structural steels is decomposed into two parts: void nucleation-induced fracture toughness (denoted as K_IC.n) and void growth-induced fracture toughness (K_IC.g). K_IC.n, defined as the stress intensity factor at which voids ahead of a crack begins to form, is calculated from crack tip strain distribution and void nucleation strain distribution. In contrast, K_IC.g is determined by the void growth from the beginning of void nucleation to void coalescence. Therefore, K_IC.g relates to the void sizes and void distribution. In this paper, the expression for K_IC.g is given from the void sizes directly from fracture surfaces. The relationship between K_IC.n, K_IC.g and K_IC is expressed in the form (K_IC)²=(K_IC.n)²+(K_IC.g)². The newly developed model was applied to the fracture toughness evaluation of three structural steels (SN490, X65 and SA440), and the theoretical calculation agrees with the experimental results.     

A model for the static fracture toughness of ductile structural steel

Fracture of ductile structural steels generally occurs after void initiation, void growth and void coalescence. In order for ductile fracture of structural steels to occur, energy must be spent to induce void initiation and void growth. Therefore, fracture toughness for ductile fracture should be contributed from void initiation and void growth. On the basis of this suggestion static fracture toughness (K_IC) of ductile structural steels is decomposed into two parts: void nucleation-induced fracture toughness (denoted as K_IC.n) and void growth-induced fracture toughness (K_IC.g). K_IC.n, defined as the stress intensity factor at which voids ahead of a crack begins to form, is calculated from crack tip strain distribution and void nucleation strain distribution. In contrast, K_IC.g is determined by the void growth from the beginning of void nucleation to void coalescence. Therefore, K_IC.g relates to the void sizes and void distribution. In this paper, the expression for K_IC.g is given from the void sizes directly from fracture surfaces. The relationship between K_IC.n, K_IC.g and K_IC is expressed in the form (K_IC)²=(K_IC.n)²+(K_IC.g)². The newly developed model was applied to the fracture toughness evaluation of three structural steels (SN490, X65 and SA440), and the theoretical calculation agrees with the experimental results.     

Numerical simulations of fracture initiation in ductile solids under mode I, dynamic loading

In this paper, an overview of some recent computational studies by the authors on ductile crack initiation under mode I, dynamic loading is presented. In these studies, a large deformation finite element procedure is employed along with the viscoplastic version of the Gurson constitutive model that accounts for the micro-mechanical processes of void nucleation, growth and coalescence. A three-point bend fracture specimen subjected to impact, and a single edge notched specimen loaded by a tensile stress pulse are analysed. Several loading rates are simulated by varying the impact speed or the rise time and magnitude of the stress pulse. A simple model involving a semi-circular notch with a pre-nucleated circular hole situated ahead of it is considered. The growth of the hole and its interaction with the notch tip, which leads to plastic strain and porosity localization in the ligament connecting them, is simulated. The role of strain-rate dependence on ductile crack initiation at high loading rates, and the specimen geometry effect on the variation of dynamic fracture toughness with loading rate are investigated.     

Numerical simulations of hole growth and ductile fracture initiation under mixed-mode loading

Numerical simulations of ductile fracture initiation caused by the interaction between a notch tip and a nearby hole under mixed-mode loading involving modes I and II are performed. Attention is restricted to plane strain, small-scale yielding conditions. The Gurson constitutive model that accounts for the ductile failure mechanisms of micro-void nucleation, growth and coalescence is employed within the framework of a finite deformation plasticity theory. The failure of the ligament connecting the notch tip and the hole by either microvoid coalescence or by intense plastic strain localization is modelled. The effect of mode-mixity on the notch tip deformation, hole growth and the critical value of J at fracture initiation is examined. The dominant failure mechanism which is operative near the notch tip for various extents of mixity of modes I and II is identified.     

基于微孔贯通细观损伤模型的金属韧性断裂分析

韧性材料断裂过程通常可看作是材料内部微孔洞的形核、扩展及相互贯通的积累。经典的Gurson- Tvergaard (GT)模型能够很好地模拟具有变形均匀、各向同性的孔洞的萌生及扩展过程;但无法模拟由孔洞贯通而引起的局部变形过程,因此需要对其修正,引入相应的孔洞贯通准则。该文采用两种贯通准则对经典GT模型进行修正,即Thomason的塑性极限载荷准则和临界等效塑性应变准则。借助用户自定义程序UMAT将采用这两种贯通准则修正的GT本构关系嵌入至商用有限元软件ABAQUS中,从而可通过对金属材料应力状态和断裂机理的分析控制孔洞的贯通。以一组含有不同缺口根半径的圆棒拉伸试验件为例,分析了该类金属构件自孔洞萌生至最终断裂的整个损伤演化过程,并与试验数据进行了对比,验证了该模型的有效性。该文还讨论了金属断裂过程中应力三轴度对微裂纹萌生与扩展的影响。     

Comparison of shear and tensile fracture in high strength aluminum alloys

A comparison was made between tensile (mode I) and shear (mode II) fracture characteristics in high strength aluminium alloys (7075-T6 and 6061-T651) using a relatively new mode II fracture specimen to evaluate the critical stress intensity factor. The enlarged plastic zone during mode II fracture required that an increased specimen thickness be used for determining K _Hc under a purely plane strain condition. Plane stress conditions prevailed in the mode II fracture of 7075-T6 with a specimen thickness less than 10 mm, while plane strain controlled mode II fracture at a thickness of 10 mm or greater. Fractographic analysis revealed a distinctive difference in the micromechanisms responsible for crack extension. Small dimples were observed only on the mode II fracture surfaces, resulting from a microvoid nucleation fracture mechanism. The mode I fracture surfaces showed a mixed distribution of dimple sizes resulting from a void growth fracture mechanism. Comparing the critical stress intensity factors, the shear mode of failure exhibited a substantially higher value than the tensile mode, resulting from the effect of the sign and magnitude of the hydrostatic stress state on the microvoid nucleation event. Zero hydrostatic tension in the mode II loading configuration helps delay microvoid nucleation, increasing the apparent toughness. The high hydrostatic tension resulting from a mode I loading configuration enhances microvoid nucleation which promotes crack propagation at relatively lower stress intensity factors.     

Constraint effects on ductile fracture processes near a notch tip under mixed-mode loading

In this work, the effect of constraint on ductile fracture process of microvoid growth and coalescence near a notch tip in a ductile material under mode I and mixed mode loading (involving modes I and II) is investigated. To this end, two sets of finite element simulations are carried out under two-dimensional plane strain conditions. In the first set, a modified boundary layer formulation is employed in which the mixed mode elastic K–T field is prescribed as remote boundary conditions. Several analyses are carried out corresponding to different values of T-stress and remote elastic mode-mixity. Next, ductile four point bend specimens subjected to mode I and mixed mode loading are considered. In both sets of simulations, the interaction between a notch tip and a pre-nucleated hole ahead of it is modelled. The background material is represented by the Gurson constitutive model and micro-void nucleation at uniformly distributed small scale particles is also taken into account. The accumulation of matrix plastic strain and porosity in the ligament between the notch tip and the hole as well as the growth of the hole are studied. Finally, the effect of crack tip constraint on the relationship between the fracture toughness and mode mixity is examined.     

A micromechanics-based model for micro-toughness estimation from dimple geometry measurements

A new model for the estimation of the micro-toughness in ductile fracture is presented. Micro-toughness is defined as the plastic work dissipated per unit fracture surface area in the material separation processes of void growth and coalescence. Stereophotogrammetric measurements of the height and width of dimples on ductile fracture surfaces are used in conjunction with the model to determine the micro-toughness. A finite element model is used to validate the analytical model. With the new model the ratio between the micro-toughness as related to the fracture surface topology and the global fracture toughness (J-integral) values become physically reasonable. The model is applied to structural steels and a metal matrix composite. Implications to computational fracture mechanics models are discussed.     

Stress triaxiality effect on void nucleation in ductile metals

The stress triaxiality effect on the strain required for void nucleation by particle‐matrix debonding has been investigated by means of micromechanical modelling. A unit‐cell model considering an elastic spherical particle embedded in an elastic‐plastic matrix was developed to the purpose. Particle‐matrix decohesion was simulated through the progressive failure of a cohesive interface. It has been shown that the parameters of matrix‐particle cohesive interface are correlated with macroscopic material properties. Here, a simple relationship for the maximum cohesive opening at interface failure as a function of material fracture toughness and yield stress has been derived. Results seem to confirm that, increasing stress triaxiality, the strain at which void nucleation is predicted to occur decreases exponentially in a similar way as for fracture strain. This result has substantial implications in modelling of ductile damage because it indicates that if the stress triaxiality is high enough, ductile fracture can occur at plastic strain lower than that necessary to nucleate damage for moderate or low stress triaxiality regime.     

Effect of strength mis-match and dynamic loading on ductile fracture initiation

It has been well known that ductile fracture of steels is accelerated by triaxial stresses. The characteristics of ductile crack initiation in steels are evaluated quantitatively using a two-parameter criterion based on equivalent plastic strain and stress triaxiality.The present study focuses on the effects of geometrical discontinuity, strength mis-match, which can elevate plastic constraint due to heterogeneous plastic straining, and loading rate on the critical condition for ductile fracture initiation using a two-parameter criterion. Fracture initiation testing has been conducted under static and dynamic loading using circumferentially notched round-bar specimens. In order to evaluate the stress/strain state in the specimens, especially under dynamic loading, a thermal elastic-plastic dynamic finite element (FE) analysis considering the temperature rise due to plastic deformation has been carried out.The tensile tests on specimens with an undermatching interlayer showed that the relationship between the critical equivalent plastic strain to initiate ductile fracture and stress triaxiality was equivalent to that obtained on homogeneous specimens under static loading. Moreover, the two-parameter criterion for ductile fracture initiation is shown to be independent of the loading rate. It was demonstrated that the critical global strain to initiate ductile fracture in specimens with strength mis-match under various loading rate can be estimated based on the local criterion, that is two-parameter criterion obtained on homogeneous specimens under static tension, by mean of FE-analysis taken into account accurately both strength mis-match and dynamic loading effects on stress/strain behaviors.     

Development of the Local Approach to Fracture over the Past 25 years: Theory and Applications

This review paper is devoted to the local approach to fracture (LAF) for the prediction of the fracture toughness of structural steels. The LAF has been considerably developed over the past two decades, not only to provide a better understanding of the fracture behaviour of materials, in particular the failure micromechanisms, but also to deal with loading conditions which cannot easily be handled with the conventional linear elastic fracture mechanics and elastic–plastic fracture mechanics global approaches. The bases of this relatively newly developed methodology are first presented. Both ductile rupture and brittle cleavage fracture micromechanisms are considered. The ductile-to-brittle transition observed in ferritic steels is also briefly reviewed. Two types of LAF methods are presented: (i) those assuming that the material behaviour is not affected by damage (e.g. cleavage fracture), (ii) those using a coupling effect between damage and constitutive equations (e.g. ductile fracture). The micromechanisms of brittle and ductile fracture investigated in elementary volume elements are briefly presented. The emphasis is laid on cleavage fracture in ferritic steels. The role of second phase particles (carbides or inclusions) and grain boundaries is more thoroughly discussed. The distinction between nucleation and growth controlled fracture is made. Recent developments in the theory of cleavage fracture incorporating both the effect of stress state and that of plastic strain are presented. These theoretical results are applied to the crack tip situation to predict the fracture toughness. It is shown that the ductile-to-brittle transition curve can reasonably be well predicted using the LAF approach. Additional applications of the LAF approach methods are also shown, including: (i) the effect of loading rate and prestressing; (ii) the influence of residual stresses in welds; (iii) the mismatch effects in welds; (iv) the warm-prestressing effect. An attempt is also made to delineate research areas where large improvements should be made for a better understanding of the failure behaviour of structural materials.     

A model for the dynamic fracture toughness of ductile structural steel

We assume in this paper that the dynamic fracture toughness K_Id of ductile structural steels is dependent on void nucleation and void growth. The void nucleation-induced dynamic fracture toughness K_Id·n and the void growth-induced dynamic fracture toughness K_Id·g were obtained by modifying the void nucleation-induced and void growth-induced static fracture toughness models, respectively, considering the effect of strain rate and local temperature. By the relationship between the void nucleation-induced dynamic fracture toughness K_Id·n and the void growth-induced dynamic fracture toughness K_Id·g((K_Id)²=(K_Id·n)²+(K_Id·g)²) dynamic fracture toughness K_Id could be quantitatively evaluated. With this model the dynamic fracture toughness of two structural steels (X65 and SA440) was assessed, and the causes for the differences between the static and dynamic fracture toughness were also discussed.     

Contribution of deformation-induced martensite to fracture appearance of austenitic stainless steel

Fracture surface commonly carries the evidence of high-energy (ductile/tough) and low-energy (brittle) regions involved in fracture history, the macroscopic appearance of a fracture surface has often been utilised to qualitatively evaluate toughness of materials. For metastable austenitic stainless steels (AISI 304LN), the degree of martensitic transformation affects the fracture appearance and thus depends critically on the strain rate. The two dimensional ductile tearing ridge pattern quantified from many tensile fractographs are observed to predict the nature of disparity in deformation and fracture responses with systematic variation in strain rate of the steel under ambient atmosphere. The spatial distribution of deformation-induced martensite under tension at various stress/strains and strain rates strongly influences void nucleation, growth, coalescence and hence, keeps the impression on the ductile tearing ridge morphologies and dimple geometries on the fracture surface, where the initial inclusion content was constant.     

A model for the dynamic fracture toughness of ductile structural steel

We assume in this paper that the dynamic fracture toughness K_Id of ductile structural steels is dependent on void nucleation and void growth. The void nucleation-induced dynamic fracture toughness K_Id·n and the void growth-induced dynamic fracture toughness K_Id·g were obtained by modifying the void nucleation-induced and void growth-induced static fracture toughness models, respectively, considering the effect of strain rate and local temperature. By the relationship between the void nucleation-induced dynamic fracture toughness K_Id·n and the void growth-induced dynamic fracture toughness K_Id·g((K_Id)²=(K_Id·n)²+(K_Id·g)²) dynamic fracture toughness K_Id could be quantitatively evaluated. With this model the dynamic fracture toughness of two structural steels (X65 and SA440) was assessed, and the causes for the differences between the static and dynamic fracture toughness were also discussed.     

Numerical modeling of the ductile-brittle transition

Numerical studies of the ductile-brittle transition are described that are based on incorporating physically based models of the competing fracture mechanisms into the material's constitutive relation. An elastic-viscoplastic constitutive relation for a porous plastic solid is used to model ductile fracture by the nucleation and subsequent growth of voids to coalescence. Cleavage is modeled in terms of attaining a temperature and strain rate independent critical value of the maximum principal stress over a specified material region of the order of one or two grain sizes. Various analyses of ductile-brittle transitions carried out within this framework are discussed. The specimens considered include the Charpy V-notch test and cracked specimens under mode I or mode II loading conditions. The fracture mode transition emerges as a natural outcome of the initial-boundary value problem solution. This revised version was published online in July 2006 with corrections to the Cover Date.     

Modeling ductile to brittle fracture transition in steels—micromechanical and physical challenges

Both scientists and engineers are very much concerned with the study of ductile-to-brittle transition (DBT) in ferritic steels. For historical reasons the Charpy impact test remains widely used in the industry as a quality control tool to determine the DBT temperature. The transition between the two failure modes, i.e. brittle cleavage at low temperature and ductile fracture at the upper shelf occurs also at low loading rate in fracture toughness tests. Recent developments have been made in the understanding of the micromechanisms controlling either cleavage fracture in BCC metals or ductile rupture by cavity nucleation, growth and coalescence. Other developments have also been made in numerical tools such as the finite element (FE) method incorporating sophisticated constitutive equations and damage laws to simulate ductile crack growth (DCG) and cleavage fracture. Both types of development have thus largely contributed to modeling DBT occurring either in impact tests or in fracture toughness tests. This constitutes the basis of a modern methodology to investigate fracture, which is the so-called local approach to fracture. In this study the micromechanisms of brittle cleavage fracture and ductile rupture are firstly shortly reviewed. Then the transition between both modes of failure is investigated. It is shown that the DBT behavior observed in impact tests or in fracture toughness specimens can be reasonably well predicted using modern theories on brittle and ductile fracture in conjunction with FE numerical simulations. The review includes a detailed study of a number of metallurgical parameters contributing to the variation of the DBT temperature. Two main types of steels are considered : (i) quenched and tempered bainitic and martensitic steels used in the fabrication of pressurized water reactors, and (ii) modern high-toughness line-pipe steels obtained by chemical variations and optimized hot-rolling conditions. An attempt is also made to underline the research areas which remain to be explored for improving the strength-toughness compromise in the development of steels.     

A numerical investigation of ductile fracture initiation in a high-strength low-alloy steel

In this work, static and drop-weight impact experiments, which have been conducted using three-point bend fracture specimens of a high-strength low-alloy steel, are analysed by performing finite-element simulations. The Gurson constitutive model that accounts for the ductile failure mechanisms of microvoid nucleation, growth and coalescence is employed within the framework of a finite deformation plasticity theory. Two populations of second-phase particles are considered, including large inclusions which initiate voids at an early stage and small particles which require large strains to nucleate voids. The most important objective of the work is to assess quantitatively the effects of material inertia, strain rate sensitivity and local adiabatic temperature rise (due to conversion of plastic work into heat) on dynamic ductile crack initiation. This is accomplished by comparing the evolution histories of void volume fraction near the notch tip in the static analysis with the dynamic analyses. The results indicate that increased strain hardening caused by strain rate sensitivity, which becomes important under dynamic loading, plays a benign role in considerably slowing down the void growth rate near the notch tip. This is partially opposed by thermal softening caused by adiabatic heating near the notch tip.     

Vapor Pressure and Residual Stress Effects on Mixed Mode Toughness of an Adhesive Film

Temperature- and moisture- induced delamination leading to popcorn package cracking is a major package reliability issue for surface-mount plastic encapsulated microcircuits (PEM). Crack propagation along one of the interfaces of a ductile adhesive joining two elastic substrates is modeled to study interface delamination and toughness of PEMs. The polymeric adhesive is stressed by remote loading and residual stress. Along the crack front, the film-substrate interface is modeled by a strip of cells that incorporates vapor pressure effects on void growth and coalescence through a Gurson porous material relation. Results show that under high levels of vapor pressure, increasing film thickness will produce smaller enhancement on the steady-state fracture resistance of the interface, also referred to as the joint toughness. Across all mode mixity levels, vapor pressure effects dominate over residual stress. The adverse effects of vapor pressure are greatest in highly porous adhesives subjected to a strong mode II component. The latter is representative of the likely state of loading in IC packages since residual stress, resulting from the film-substrate thermal mismatch, induces a predominantly mode II component.     

Modeling of hydrogen-assisted ductile crack propagation in metals and alloys

This paper presents a finite element study of the hydrogen effect on ductile crack propagation in metals and alloys by linking effects at the microstructural level (i.e., void growth and coalescence) to effects at the macro-level (i.e., bulk material deformation around a macroscopic crack). The purpose is to devise a mechanics methodology to simulate the conditions under which hydrogen enhanced plasticity induces fracture that macroscopically appears to be brittle. The hydrogen effect on enhanced dislocation mobility is described by a phenomenological constitutive relation in which the local flow stress is taken as a decreasing function of the hydrogen concentration which is determined in equilibrium with local stress and plastic strain. Crack propagation is modeled by cohesive elements whose traction separation law is determined through void cell calculations that address the hydrogen effect on void growth and coalescence. Numerical results for the A533B pressure vessel steel indicate that hydrogen, by accelerating void growth and coalescence, promotes crack propagation by linking simultaneously a finite number of voids with the crack tip. This “multiple-void” fracture mechanism knocks down the initiation fracture toughness of the material and diminishes the tearing resistance to crack propagation.     

A simple damage-accumulation model for constraint effects on ductile fracture

A simple model is presented to account for the effects of void-type damage on crack initiation and propagation in ductile steels under plane strain conditions by virtue of elementary fracture mechanics solutions. Multiple primary voids from large inclusions are uniformly distributed ahead of the crack tip. The growth of these primary voids is followed by nucleation of a large population of secondary voids from second-phase particles. A critical accumulative damage based on the length ratio of the damage zone to the spacing of primary voids, is employed as a failure criterion, including contributions from two populations of voids. Damage accumulation depends much on the strain and stress states such as stress triaxilities, which are extracted from existing results instead of detailed computation. Results show the dependence of fracture toughness on the size of damage zones associated with constraints. Initiation of crack growth is insensitive to the constraints since nucleation of fine voids is determined by local deformation. The model captures the transition in mechanisms from void-by-void growth to multiple void interactions in terms of a decreasing trend in the slopes of fracture resistance curves. At high constraints and large damage zone, a steady-state crack advance is identified with constant toughness. Damage accumulation from the growth of primary voids determines subsequent crack growth resistance and the study demonstrates its dependences on the crack-tip constraints.