Process Zone Model Research Articles

Improved size effect law (SEL) considering size-dependent fracture process zone (FPZ) for quasi-brittle materials

Establishing a mechanistic model to simultaneously capture the descending size effect (DSE) and the change from DSE to the ascending size effect (ASE) remains a challenging issue for quasi-brittle materials. A size-dependent fracture process zone (FPZ) model is proposed and verified by experimental and simulative results. Subsequently, the size effect law (SEL) of unnotched specimens is improved by considering the size-dependent FPZ model, which is termed the improved SEL in this paper. Parametric studies are conducted for a better understanding of the improved SEL. It is found that the underlying mechanism of the DSE and the change from DSE to ASE is the competition between the relative rates of FPZ and specimen size change with respect to specimen size. The ASE is obtained when the relative rate of FPZ change is higher than that of specimen size. Conversely, the DSE is observed. No size effect exists when the relative rate of FPZ change is equal to that of specimen size. Experimental and simulative results are adopted to validate the improved SEL of unnotched specimens. The validation of the improved SEL indicates that the improved SEL not only accurately predicts the DSE, but also correctly captures the change from DSE to ASE. In addition, the size effect of nominal strength with different maximum aggregate size is well captured by the improved SEL. The fitting parameters of the improved SEL lie in the given interval. By comparing the determination coefficients R2 of the SEL, unified size effect law (USEL), and improved SEL, it is found that the R2 of the improved SEL is higher than that of the SEL for the DSE and is close to that of the IUSEL for the change from DSE to ASE. Therefore, it is recommended that engineers and researchers use the improved SEL to describe the DSE and the change from DSE to ASE of unnotched specimens.

Mode I fracture behavior of heterogeneous granite: Insights from grain-based FDEM modelling

The failure of brittle rock has a significant influence on engineering stability. The purpose of this study is to understand the progressive fracture mechanism of heterogeneous granite from a mesoscopic perspective. In the present work, the fracture process zone (FPZ) model is used to characterize the constitutive relationship of rock cracking in the combined finite-discrete element method (FDEM). Moreover, the breakable grain-based model (bGBM) is established to study the fracture behavior of granite via the semi-circular bending (SCB) tests. To rebuild the meso-structure of granite specimens, an algorithm that considers the mesoscopic grain geometry characteristics and grain contact mechanical properties is utilized. Then, three classic examples, namely, a uniaxial compressive test, a Brazilian splitting test and a semi-circular bending test, are investigated with the numerical model. A good agreement of the load–displacement curves and crack propagation paths can be found between the simulation and laboratory tests. The meso-heterogeneity of granite cause the macroscopic fracture surface of the slit tip to be nearly upright, with local roughness and zigzag. The slit length has a significant effect on the damage distribution range of the SCB specimen, and the peak load and mode I fracture toughness decreases with increasing slit length and supporting span. The accurate measurement of the mode I fracture toughness of SCB specimens needs to consider the FPZ, and the average increment is 39% and 41% under different slit length and supporting span conditions, respectively.

Investigation of the size of the fracture process zone and the cleavage stress in cracked steel parts

AbstractThe study is devoted to the development of methods for predicting the brittle fracture of a steel part with a crack. To describe the limit state of the fracture process zone, a mathematical model of the fracture process zone in an elastic–plastic stress state and the generalized brittle fracture theory have been used. The cleavage stress and the size of the fracture process zone are used as parameters for the fracture toughness of the material. A finite element analysis approach was developed to determine these parameters by considering the elastic–plastic stress state of cracked specimens. An analytical procedure for calculating the above parameters for low‐carbon and low‐alloy steels is given. The proposed models allow the analytical calculation of critical values of the stress intensity factor for specimens with cracks at negative temperatures. The development of this study is linked to the improvement of the technology for determining the physical strength criteria of materials. The application of the proposed models makes it possible to create a methodology for predicting crack resistance of welded structures of arctic design considering their geometry and structural and technological characteristics.

A Time Dependent Process Zone Model for Slow Crack Growth of Polyethylene Pipe Material

Polyethylene (PE) pipe is widely used in water supply and gas transportation engineering. Its fracture behavior is very important for the safe operation of the pipeline. The objective of this work is to simulate the slow crack growth (SCG) process of PE pipe material via a time dependent crack-tip process zone model. To achieve this end, the crazing damage caused by stress concentration at crack tip of PE material is taken into account, the stress on the bulk/craze interface layer is supposed to be uniformly distributed due to the micro necking mechanism of the layer, and a linear crack growth kinetics is used. In order to describe the delay characteristics of the fracture process of PE materials, the fracture surface energy is considered as an exponential decay function of time, which is attributed to the creep damage of the craze fibrils. A simulation algorithm of the proposed process zone model is suggested using iterative method. The model is verified by comparing the simulation with the discontinuous SCG behavior reported in the literature.

An analytical model of fracture process zone to explain why crack-tip opening angle works

An analytical model of fracture process zone (FPZ) was proposed to explore the intrinsic meaning of the “constant crack-tip opening angle (CTOA)” fracture criterion. A relationship between critical CTOA and the essential work of fracture (EWF) was then established. According to above relationship, critical CTOA is found to represent the critical state of FPZ. During stable crack growth, FPZ is fixed since stress state and material properties are changeless, and this is why “constant CTOA” works. In the case external boundary far from the FPZ, the FPZ will only depend on thickness and material properties, and then critical CTOA will own in-plane geometry transferability. In addition, the linear relationship between critical CTOA and local fracture strain is also explained.

An improved theoretical process-zone model for delayed hydride cracking initiation at a blunt V-notch

Delayed hydride cracking (DHC) is an important concern for pressure tubes used in nuclear reactors. In this paper, an improved analytical process-zone model is developed based on the deformation fracture criteria. A V-notch with rounded root, which is widely adopted in mechanical testing of DHC, is considered and the proposed model includes the effect of both notch angle and tip radius. Comparisons with experiments show that the proposed model has a prediction accuracy closer to the current engineering process-zone model but with slightly less conservatism. The model is extended to account for plasticity and constraint effects at the flaw tip by introducing an empirical factor that depends on key material and geometric parameters.

Multiscale crystal defect dynamics: A coarse-grained lattice defect model based on crystal microstructure

Crystal defects have microstructure, and this microstructure should be related to the microstructure of the original crystal. Hence each type of crystals may have similar defects due to the same failure mechanism originated from the same microstructure, if they are under the same loading conditions. In this work, we propose a multiscale crystal defect dynamics (MCDD) model that models defects by considering its intrinsic microstructure derived from the microstructure or material genome of the original perfect crystal. The main novelties of present work are: (1) the discrete exterior calculus and algebraic topology theory are used to construct a scale-up (coarse-grained) dual lattice model for crystal defects, which may represent all possible defect modes inside a crystal; (2) a higher order Cauchy–Born rule (up to the fourth order) is adopted to construct atomistic-informed constitutive relations for various defect process zones, and (3) an hierarchical strain gradient theory based finite element formulation is developed to support an hierarchical multiscale cohesive (process) zone model for various defects in a unified formulation. The efficiency of MCDD computational algorithm allows us to simulate dynamic defect evolution at large scale while taking into account atomistic interaction. The MCDD model has been validated by comparing of the results of MCDD simulations with that of molecular dynamics (MD) in the cases of nanoindentation and uniaxial tension. Numerical simulations have shown that MCDD model can predict dislocation nucleation induced instability and inelastic deformation, and thus it may provide an alternative solution to study crystal plasticity.

The micro-damage process zone during transverse cortical bone fracture: No ears at crack growth initiation

ObjectiveApply high-resolution benchtop micro-computed tomography (micro-CT) to gain greater understanding and knowledge of the formation of the micro-damage process zone formed during traverse fracture of cortical bone. MethodsBovine cortical bone was cut into single edge notch (bending) fracture testing specimens with the crack on the transverse plane and oriented to grow in the circumferential direction. We used a multi-specimen technique and deformed the specimens to various individual secant modulus loss levels (P-values) up to and including maximum load (Pmax). Next, the specimens were infiltrated with a BaSO4 precipitation stain and scanned at 3.57-μm isotropic voxel size using a benchtop high resolution-micro-CT. Measurements of the micro-damage process zone volume, width and height were made. These were compared with the simple Irwin's process zone model and with finite element models. Electron and confocal microscopy confirmed the formation of BaSO4 precipitate in micro-cracks and other porosity, and an interesting novel mechanism similar to tunneling. ResultsMeasurable micro-damage was detected at low P values and the volume of the process zone increased according to a second order polynomial trend. Both width and height grew linearly up to Pmax, at which point the process zone cross-section (perpendicular to the plane of the crack) was almost circular on average with a radius of approximately 550µm (approximately one quarter of the unbroken ligament thickness) and corresponding to the shape expected for a biological composite under plane stress conditions. ConclusionThis study reports details of the micro-damage fracture process zone previously unreported for cortical bone. High-resolution micro-CT enables 3D visualization and measurement of the process zone and confirmation that the crack front edge and process zone are affected by microstructure. It is clear that the process zone for the specimens studied grows to be meaningfully large, confirming the need for the J-integral approach and it does not achieve steady state at Pmax in most specimens. With further development, this approach may become valuable towards better understanding the role of the process zone in cortical bone fracture and the effects of relevant modifications towards changes in fracture toughness in a cost effective way.

Puncture mechanics of soft solids

Gels and other soft elastic networks are a ubiquitous and important class of materials whose unique properties enable special behavior, but generally elude characterization due to the inherent difficulty in manipulating them. An example of such behavior is the stability of gels to large local deformations on their surface. This paper analyzes puncture of model soft materials with particular focus on the force response to deep indentation and the critical load for material failure. Large-strain behavior during deep indentation is described with a neo-hookean contact model. A fracture process zone model is applied to the critical load for puncture. It is found that the indenter geometry influences the size of the fracture process zone, resulting in two distinct failure regimes: stress-limited and energy-limited. The methods outlined in this paper provide a simple means for measuring Young's modulus, E, as well as the material's maximum cohesive stress, σ0, fracture energy, Γ0, and the intrinsic length scale linking the two, l0, all without requiring specialized sample preparation.

Multiscale modeling and prediction of bonded joint failure by using an adhesive process zone model

In this work, a three-dimensional multiscale adhesive process zone model (APZM) is used to simulate dynamic failure process of bonded joint structures. APZM combines the ideas of the cohesive zone model (CZM), the Cauchy–Born rule, and the so-called virtual internal bond (VIB) theory to predict failures of bonded joints that involves adhesive failure, cohesive failure, and mixture of both. The proposed APZM has some unique advantages to describe mechanical behaviors of bonded joints under general loading conditions. First, in contrast to conventional FEM model, APZM model can simulate dynamic fracture process of structure without remeshing. Second, APZM replaces the ad-hoc traction–separation laws of interface used in CZM with full three-dimensional interphase model, which is based on the VIB theory. Consequently, APZM can naturally capture both mixed failure modes as well as mixture failure mode under complex loading conditions. Third, an empirical elastic energy density function for macromolecular polymers was constructed, and its material parameters are obtained by calibrating the model with material properties measured from experiments such as under pure tension and shear tests. In order to validate APZM model and to predict stress field in adhesive layer accurately, a series of numerical simulations of bonded joints under shear, tension and mixed loading conditions have been conducted. The numerical results indicate that APZM can accurately predict the failure modes as well as the dynamics fracture process of bonded joints.

Multiscale crystal defect dynamics: a dual-lattice process zone model

In this work, we present the theoretical and computational formulations of a multiscale crystal defect dynamics (MCDD) for the simulation of crystal defects at small scales. The main novelties of the proposed MCDD are: (1) We use the dual-lattice tessellation to construct a dual-lattice process zone model that can represent different types of crystal defects in a single crystal; (2) We adopt a fourth-order (four scales) hierarchical strain gradient theory to model constitutive behaviours of various defect process zones, in which the atomistic-informed higher order Cauchy–Born rule is employed, and (3) We employ the Barycentric finite element technique to construct finite element shape functions for polygonal and polyhedral process zone elements. The proposed MCDD method provides an efficient and viable alternative for both molecular dynamics and dislocation dynamics in simulations of defect evolutions such as void growth, dislocation nucleation, and fracture. In particular, MCDD offers a mesoscale description for dynamic lattice microstructure, defect microstructure, and their interactions. The method offers a possible solution for studying nanoscale and mesoscale crystalline plasticity.

Application of Multiscale Process Zone Model to Simulate Fracture in Polycrystalline Solids

In this work, an early proposed atomistic-based multiscale process zone model is revised and employed to simulate crack propagation and spall fracture in polycrystalline solids. The multiscale process zone model is capable of describing heterogenous materials by incorporating the effect of inhomogeneities such as grain boundaries, slip lines and inclusions. A consistent depletion potential resulting from fundamental principles in colloidal physics is used to describe the cohesive laws for both the grain interfaces and process zones in bulk materials, which provides microstructure-based interface potentials in both normal and tangential directions with respect to finite element boundary separations in contrast to conventional cohesive methods. The polycrystalline microstructure are generated by using the Voronoi tessellations. Two different approaches of treating the process zone are proposed. The multiscale process zone model is implemented in a Lagrange framework based on the Galerkin weak form formulation. In addition, to eliminate the zero-energy modes and avoid shear locking in the interphase elements, a reduced integration technique is adopted in simulations. Numerical simulations on crack propagation in materials with various cohesive strengths have been carried out, and they can describe both inter-granular and trans-granular fractures. Finally, the spall-fracture of a specimen under high-impact load is captured using the proposed multiscale process zone model.

Determining of three collinear cracks opening displacement using the process zone model

The general failure of structures is often preceded by the growth and coalescence of intermediate cracks. In this work, a model with process zone is used to study the deformed state of an infinite isotropic body with three collinear cracks. A numerical algorithm is presented to obtain crack opening displacements effectively. The problem is analyzed for all possible cases of mutual location of the cracks and different levels of loading. The numerical solution shows negligible influence of two cracks coalescence process on the opening displacement of the third crack. An example of the results implementation to calculate crack initiation duration in a problem for viscoelastic body is given.

A three‐dimensional atomistic‐based process zone model simulation of fragmentation in polycrystalline solids

SUMMARYA three‐dimensional atomistic‐based process zone model (APZM) is used to simulate high‐speed impact induced dynamic fracture process such as fragmentation and spall fracture. This multiscale simulation model combines the Cauchy–Born rule, colloidal crystal process model, and micromechanics homogenization technique to construct constitutive relations in both grains and grain boundary at mesoscale. The proposed APZM has some inherent advantages to describe mechanical behaviors of polycrystalline solids. First, in contrast to macroscale phenomenological constitutive models, the APZM takes into account atomistic binding energy and atomistic lattice structure. In particular, the electron density related embedded atom method (EAM) potential has been adopted to describe interatomistic interactions of metallic polycrystalline solids in bulk elements; second, a mixed type of EAM potential and colloidal crystal depletion potential is constructed to describe heterogeneous microstructure in the process zone; third, the atomistic potential in both bulk material and process zone has the same atomistic origin, and hence, the bulk and process potentials are self‐consistent. The simulation of dynamic fracture process of a cylinder made of aluminum powder metallurgy (P/M) alloy during high‐speed impact/penetration is carried out, and numerical results demonstrate that APZM finite element method has remarkable ability to accurately capture complex three‐dimensional fragmentation formation and damage morphology. Copyright © 2012 John Wiley & Sons, Ltd.

Modeling the fracture process zone near a crack tip in a nonlinear elastic body

The model of a fracture process zone near the tip of a mode I crack in a nonlinear elastic body is proposed. Using the numerical solution of an appropriate boundary-value problem, the effect of the fracture process zone on a crack opening displacement is examined

An Investigation into the Use of an Embedded Process Zone Model for Predicting the Structural Behaviour of Adhesive Bonded Joints

The study presented in this paper was carried out to assess the use of an embedded process zone based model in a commercial finite element code for predicting the behaviour of adhesively bonded structures. The relevant adhesive properties were measured using a variety of test methods and the results applied to the analysis of a single lap joint. Having demonstrated satisfactory accuracy in simulating the behaviour of the single lap joint the same methodology was then applied to a more complex structure. The structure used was a T shaped structure formed from two adhesively bonded aluminium rails. Despite some variability in the test results acceptable correlation with the analysis results was again achieved. The effects of variability in the adhesive material data on the output from the Finite Element analysis were investigated using a statistical study. This showed only a limited sensitivity to the interface toughness parameter.

Delayed Hydride Cracking Initiation at Notches in Zr-2.5Nb Alloys

Delayed hydride cracking (DHC) is an important crack initiation and growth mechanism in Zr-2.5Nb alloy pressure tubes of CANDU nuclear reactors. DHC is a repetitive process that involves hydrogen diffusion, hydride precipitation, growth, and fracture of a hydrided region at a flaw tip. In-service flaw evaluation requires analyses to demonstrate that DHC will not initiate from the flaw. The work presented in this paper examines DHC initiation behavior from V-notches with root radii of 15 μm, 30 μm, and 100 μm, which simulate service-induced debris fretting flaws. Groups of notched cantilever beam specimens were prepared from two unirradiated pressure tubes hydrided to a nominal hydrogen concentration of 57 wt. ppm. The specimens were loaded to different stress levels that straddled the threshold value predicted by an engineering process-zone (EPZ) model, and subjected to multiple thermal cycles representative of reactor operating conditions to form hydrides at the notch tip. Threshold conditions for DHC initiation were established for the notch geometries and thermal cycling conditions used in this program. Test results indicate that the resistance to DHC initiation is dependent on notch root radius, which is shown by optical metallography and scanning electron microscopy to have a significant effect on the distribution and morphology of the notch-tip reoriented hydrides. In addition, it is observed that one tube is less resistant to DHC initiation than the other tube, which may be attributed to the differences in their microstructure and texture. There is a reasonable agreement between the test results and the predictions from the EPZ model.

Multi-length scale micromorphic process zone model

The prediction of fracture toughness for hierarchical materials remains a challenging research issue because it involves different physical phenomena at multiple length scales. In this work, we propose a multiscale process zone model based on linear elastic fracture mechanics and a multiscale micromorphic theory. By computing the stress intensity factor in a K-dominant region while maintaining the mechanism of failure in the process zone, this model allows the evaluation of the fracture toughness of hierarchical materials as a function of their microstructural properties. After introducing a multi-length scale finite element formulation, an application is presented for high strength alloys, whose microstructure typically contains two populations of particles at different length scales. For this material, the design parameters comprise of the strength of the matrix–particle interface, the particle volume fraction and the strain-hardening of the matrix. Using the proposed framework, trends in the fracture toughness are computed as a function of design parameters, showing potential applications in computational materials design.

Peeling of Elastic Tapes: Effects of Large Deformations, Pre-Straining, and of a Peel-Zone Model

A peel model for non-linear elastic tapes is presented which accounts for large deformations and for pre-straining. The large deformation setting is a new feature of modelling, which would be of interest for applications related to soft polymers and tissues. The conditions for having quasistatic-steady debonding or dynamic catastrophic debonding are determined in terms of the loading variables (peel angle and peeling force). The decohesion energy associated with a given process-zone model is included in the formulation of the peeling model. The predictions of various decohesion laws are discussed with respect to experimental results in the literature. Finally, the adhesion of a gecko is analysed and the maximum adhesion force of a single spatula is evaluated. The result correlates well with the maximum experimental pulling force reported in the literature for a gecko's seta.

Model of the fracture process zone at the tip of a crack reaching the nonsmooth interface between elastic media

The paper is concerned with the fracture process zone at the tip of a crack at the nonsmooth interface between isotropic elastic media. A plane symmetric problem is formulated. The zone is modeled by lines of discontinuity of the normal displacement at the interface. The exact solution of the elastic problem is found by the Wiener-Hopf method