Predict Crack Nucleation Research Articles

Predicting crack nucleation in commercially pure titanium using orientation imaging microscopy and machine learning

Due to the prohibitively long experimental and simulation times, dwell fatigue (DF) failure prediction in titanium and its alloys is a challenging task. Since most of these failures have a microstructural level origin, this work focusses on utilizing minimal experiments and machine learning for predicting failure initiation points in a given microstructure. Failure initiation points in commercially pure titanium were identified using interrupted tensile and DF tests. Orientation imaging data was used to train a Random Forest model to calculate the relative importance of various grain orientation-based features to crack nucleation. Subsequently a predictive model for identifying locations that are likely to form a DF crack in a microstructure is developed.

Fatigue cracking behavior and life assessment of TC11 titanium alloy in very high cycle regime at two working temperatures

Axial loading fatigue tests were conducted with two stress ratios to investigate fracture surface behavior and associated failure analysis governing crack nucleation of TC11 titanium alloy at two working temperatures, spanning high-cycle and very high-cycle fatigue regimes. Furthermore, scanning electron microscopy, optical microscopy, and electron-backscattered diffraction techniques were employed to analyze the cracking mechanism. The interior failure is attributed to the cleavage of the large equiaxed αp-grains and facet-facet cluster area-fisheye formation. Moreover, the crack growth threshold values and the transition sizes from small to long cracks decrease with temperature rise. In addition, small cracks follow the path that requires minimum energy for propagation as per the microstructural orientation and are governed by maximum shear stress, resulting in the formation of crystallographic facets. Based on the analysis above, the interior fracture mechanism was summarized as related to the microstructure characteristics. Considering the fatigue cracking behavior and microstructural features, a model for predicting crack nucleation life is developed, exhibiting a better consistency between predicted and experimental fatigue lives.

A dislocation-based damage-coupled constitutive model for single crystal superalloy: Unveiling the effect of secondary orientation on creep life of circular hole

Circular holes in single crystal (SX) turbine blades are susceptible to creep failure at high temperatures, due to the stress concentrations near the holes. In this study, a dislocation-based damage-coupled constitutive model for SX superalloys is developed, validated, and applied to unveil the effect of secondary orientation on the creep life of circular holes. The structure-induced geometrically necessary dislocations (GND) density resulting from the macroscopic strain gradient is incorporated. The dissipated energy is employed as the indicator to predict crack nucleation. Initially, the specimens without a hole are employed to calibrate the parameters and validate the model in the absence of structure-induced GND. Creep experiments incorporating the digital image correlation technique are conducted on the specimens with a hole under different secondary orientations, which aims to validate the simulated strain distribution, crack nucleation location, and creep life under the influence of structure-induced GND. The results indicate that the incorporation of structure-induced GND contributes to mitigating the conservatism in the creep life prediction of circular holes. Because, the GND can enhance dislocation hardening near the hole, extending the predicted life and improving the accuracy of life prediction. Meanwhile, both experiments and simulations indicate that the secondary orientation influences the crack nucleation locations at the hole edge. The variation in the creep life at different secondary orientations is attributed to the changes in both the maximum value and uniformity of resolved shear stresses distributed across slip systems. Finally, the model is applied to simulate the creep behavior of a circular hole under various secondary orientations, stresses, and temperatures. An empirical model is developed to rapidly evaluate the creep life of a circular hole in the SX superalloy, which facilitates the engineering application of the proposed model.

An elastoplastic phase-field model for dynamic fracture of nickel-based super-alloys

This paper presents a elastoplastic phase-field model for predicting crack nucleation, propagation, and branching, among other things, in elastoplastic solids subjected to dynamic loading. During the entire fracture process of the nickel-based super-alloys, with the accumulation of plastic strain, to some extent the elastic response of the material is reduced and the rate of phase-field evolution is affected, this means that the elastic strength and phase-field evolution of the material will be influenced by the yield surface and the hardening function. Therefore, we construct elastic and plastic energy degradation functions to more accurately reflect the effects of mechanical fields on the damage field, which distinguish between two successive failure mechanisms: (i) elastic strain and (ii) simultaneous elastoplastic localization deformation. In a variational framework, we derive the governing equations and the corresponding weak forms. Then, damage evolution criterion combining elastoplastic and resistance energies and a plastic yielding criterion are derived. From a numerical point of view, we give model parameters’ selection criteria. Finally, the proposed model is applied to some impact scenarios with varying impact velocities or pre-existent cracks. The comparison of numerical and experimental results shows it can be easily used for identifying material gradation profiles that manipulate crack propagation.

Numerical aspects of phase field models for low-temperature fracture in asphalt mixtures

Unlike the cohesive interface element model, the phase field model (PFM) is a newly developed computational model which provides a unified approach to predicting crack nucleation, propagation, coalescence and branching without any ad-hoc criterion. Over the years, several variants of the phase field model are presented. This paper aims to investigate the suitability of different phase field models and determine the optimal characteristic functions/model parameters for low-temperature fracture in asphalt mixtures. The analysis results of the phase field method (which belongs to a class of diffuse damage models) are also compared with the interface element model (which belongs to a class of discrete damage models). The models are compared by examining the governing equations and performing numerical simulations on single-edge notch specimens. Furthermore, various aspects of cohesive zone model (CZM) based PFM are discussed including the type of softening laws and damage growth under uniform/non-uniform stress states. It is concluded that brittle phase field models are not fully capable to predict fracture in asphalt mixtures even at low temperatures.

A comparative study between phase‐field and micromorphic gradient‐extended damage models for brittle fracture

AbstractTo circumvent a mesh dependency of damage models, non‐local approaches such as phase‐field and gradient‐extended damage models have shown a good capability and attracted a lot of attention for modeling fracture. These models can predict crack nucleation, kinking, and branching. The gradient‐extended formulation proposed by [1, 2], which includes a micromorphic degree of freedom for damage, is connected to a phase‐field damage model presented in [3]; by connecting fracture parameters in brittle fracture. The latter is followed by comparing the thermodynamic consistency of these models. Despite having similarities in the formulation, gradient‐extended models differ from the standard phase‐field ones by having a damage threshold. Besides that, the local iteration exists in the gradient‐extended damage models. By employing the cohesive phase‐field model or the Angiotensin type 1 (AT1), a damage threshold appears in the formulation; by having a linear term for damage in the crack density function, see [4,5,12]. A comparison between these models is made, by taking several numerical examples and comparing their responses in a quasi‐static case. Moreover, the feasibility of different responses is addressed when one uses a standard Newton‐Raphson solver or the arc‐length one for solving a boundary value problem.

An asynchronous variational integrator for the phase field approach to dynamic fracture

AbstractThe phase field approach is widely used to model fracture behaviors due to the absence of the need to track the crack topology and the ability to predict crack nucleation and branching. In this work, the asynchronous variational integrator (AVI) is adapted for the phase field approach of dynamic brittle fracture. The AVI is derived from Hamilton's principle and allows each element in the mesh to have its own local time step that may be different from others'. While the displacement field is explicitly updated, the phase field is implicitly solved, with upper and lower bounds strictly and conveniently enforced. In particular, two important variants of the phase field approach, the AT1 and AT2 models, are equally easily implemented. Several benchmark problems are used to study the performances of both the AT1 and AT2 models, and the results show that the AVI for the phase field approach significantly speeds up the computational efficiency and successfully captures the complicated dynamic fracture behavior.

A general framework for decomposing the phase field fracture driving force, particularised to a Drucker–Prager failure surface

Due to its computational robustness and versatility, the phase field fracture model has become the preferred tool for predicting a wide range of cracking phenomena. However, in its conventional form, its intrinsic tension–compression symmetry in damage evolution prevents its application to the modelling of compressive failures in brittle and quasi-brittle solids, such as concrete or rock materials. In this work, we present a general methodology for decomposing the phase field fracture driving force, the strain energy density, so as to reproduce asymmetrical tension–compression fracture behaviour. The generalised approach presented is particularised to the case of linear elastic solids and the Drucker–Prager failure criterion. The ability of the presented model to capture the compressive failure of brittle materials is showcased by numerically implementing the resulting strain energy split formulation and addressing four case studies of particular interest. Firstly, insight is gained into the capabilities of the model in predicting friction and dilatancy effects under shear loading. Secondly, virtual direct shear tests are conducted to assess fracture predictions under different pressure levels. Thirdly, a concrete cylinder is subjected to uniaxial and triaxial compression to investigate the influence of confinement. Finally, the localised failure of a soil slope is predicted and the results are compared with other formulations for the strain energy decomposition proposed in the literature. The results provide a good qualitative agreement with experimental observations and demonstrate the capabilities of phase field fracture methods to predict crack nucleation and growth under multi-axial loading in materials exhibiting asymmetric tension–compression fracture behaviour.

A new discrete element model for rock-like materials

Rock-like materials such as sandstone, concrete and ceramic are composed of cemented discrete particles. As such, the discrete element method can effectively characterize the fracturing behaviour of those materials. This paper presents a new discrete element model for rock-like materials. The model is superior to most discrete element-based models in algorithm simplicity since a simple translational movement of particles and a simple tensile yield criterion defined in the model are sufficient to capture the behaviours of a rock-like material. Thus, the rotation and torque calculations can be safely removed from the algorithm. In addition, the model has advantage over most discrete element models in stress analysis, and the stress distribution predicted by the proposed model agrees very well with both the analytical and finite element solutions. Besides, the crack patterns predicted by the model agree well with the experimental observations. Therefore, the model is more effective in predicting crack nucleation, growth and propagation of rock-like materials.

Development of microstructure-sensitive damage models for zirconium polycrystals

The incorporation of four different microstructure-sensitive damage mechanisms into a crystal plasticity finite element model is described in detail. The nucleation and propagation of cracks are based on (1) the local principal stress and normal to the corresponding principal plane, (2) the local principal plastic strain and normal to the corresponding principal plane, (3) the local maximum slip and normal to the predominant slip system, and (4) the energy stored in dislocations and normal to the predominant slip system. To study the performance of each model in predicting crack nucleation and propagation, the “as-measured” microstructure in the vicinity of a sharp notch in a pure zirconium specimen is imported into the crystal plasticity model. The numerical results are compared with those measured by the electron backscatter diffraction technique. This is followed by a numerical study of the effects of crystal orientation on the prediction of each model for a notched single crystal zirconium specimen. For the specimen texture studied here, results show that the principal stress and the maximum slip methods can correctly predict the location of major cracks, where only the latter replicates the correct direction of crack propagation. Predictions from the energy method or the principal plastic strain method mainly coincide with the minor cracks or those that propagate at higher applied strains.

A mechanistic and stochastic approach to fatigue crack nucleation in coarse grain RR1000 using local stored energy

AbstractThe crystal plasticity finite element (CPFE) method is used in conjunction with a critical local stored energy criterion to predict crack nucleation life for Coarse Grain (CG) nickel superalloy RR1000. Artificial representative microstructures are generated using Dream3D, and through simulation of multiple microstructural instantiations, a distribution of simulated fatigue response is generated. Fatigue of CG RR1000 is studied at 300°C and 700°C and at two R ratios of R = 0.1 and R = −1 giving a range of conditions to test the stored energy method. At higher temperature failure frequently occurs from inclusions, these are represented in the model by adding an inclusion with cohesive zones between inclusion and matrix. The results at 300°C are very good with the one parameter model (the critical stored energy) able to predict the mean, slope and distribution of fatigue data. At 700°C, the results are also good; however, fatigue life at high strain amplitude is overpredicted.

A coupled 3D wear and fatigue numerical procedure: Application to fretting problems in ultra-high strength steel wires

This work presents a coupled 3D wear and fatigue numerical procedure for fretting problems in ultra-high strength steel wires that combines Archard’s wear equation with the Smith–Watson–Topper parameter to predict crack nucleation. For total life prediction, a mode I crack propagation based on the weight function method was used. To assess fretting fatigue lifetime, several experimental campaigns were run. The numerical results were in good agreement with the fretting fatigue experimental results. Thus, this study provides a 3D numerical methodology to study the combined effects of wear and fatigue in fretting with a case study in ultra-high strength steel wires.

An energy-based peridynamic model for fatigue cracking

Fatigue design assessment is a crucial step in the design process of ships and offshore structures. To date, the stochastic approach is commonly used to calculate the total lifetime accumulated fatigue damage and the probability of fatigue failure for the structures. Meanwhile, the details of damage initiation and propagation are infrequently investigated. In terms of predicting crack growth, the traditional approaches face conceptual and mathematical difficulties in terms of predicting crack nucleation and growth, especially for multiple crack paths because the equations in classical continuum mechanics are derived by using spatial derivatives. Peridynamics is a non-local theory using the integral equations rather than differential equations which makes it suitable for damage prediction. In this study, a novel energy-based peridynamic model for fatigue cracking is proposed. The definition of cyclic bond energy release rate range and the energy-based peridynamic fatigue equations for both phases crack initiation and crack growth phases are introduced. For validation, first, a problem of mode-I fatigue crack growth is investigated. Next, different mixed-mode fatigue damages are also investigated and the peridynamic results are compared with the experimental results.

Revisiting nucleation in the phase-field approach to brittle fracture

Twenty years in since their introduction, it is now plain that the regularized formulations dubbed as phase-field of the variational theory of brittle fracture of Francfort and Marigo (1998) provide a powerful macroscopic theory to describe and predict the propagation of cracks in linear elastic brittle materials under arbitrary quasistatic loading conditions. Over the past ten years, the ability of the phase-field approach to also possibly describe and predict crack nucleation has been under intense investigation. The first of two objectives of this paper is to establish that the existing phase-field approach to fracture at large — irrespectively of its particular version — cannot possibly model crack nucleation. This is so because it lacks one essential ingredient: the strength of the material.The second objective is to amend the phase-field theory in a manner such that it can model crack nucleation, be it from large pre-existing cracks, small pre-existing cracks, smooth and non-smooth boundary points, or within the bulk of structures subjected to arbitrary quasistatic loadings, while keeping undisturbed the ability of the standard phase-field formulation to model crack propagation. The central idea is to implicitly account for the presence of the inherent microscopic defects in the material — whose defining macroscopic manifestation is precisely the strength of the material — through the addition of an external driving force in the equation governing the evolution of the phase field. To illustrate the descriptive and predictive capabilities of the proposed theory, the last part of this paper presents sample simulations of experiments spanning the full range of fracture nucleation settings.

Modeling microfracture evolution in heterogeneous composites: A coupled cohesive phase-field model

Modeling micro-crack evolution in highly heterogeneous solids has been a major challenge in brittle materials owing to their complex microstructures and the complicated interactions between their components. The present work aims to address this challenging task through the development of a novel coupled cohesive phase-field model that can accurately predict the evolution of microfracture and describe interfacial de-bonding in quasi-brittle composites. As a crucial part of our modeling framework, the interface is described by an auxiliary interface variable, thus the interface properties can be regularized. The developed model has the following novelties: (1) the coupled cohesive phase field method is accomplished by implementing a gradient damage formulation to predict crack nucleation and propagation in quasi-brittle solids; (2) the interface properties in complex heterogeneities are regularized by the interaction between matrix and inclusions properties, as well as the width of the interface; and (3) it can precisely predict the crack evolution (crack initiation, propagation, deflection into the matrix) in quasi-brittle heterogeneous solids. Particularly, the proposed model is validated using our implemented experimental results, from which the micro-crack trajectories in fiber-cement composites were observed. The proposed approach shows great potentials in predicting the fiber de-bonding as well as the micro-crack kinking path in complicated quasi-brittle materials.

A Fatigue Life Model for Predicting Crack Nucleation at Inclusions in Ni-Based Superalloys

Engineering alloys such as Ni-based alloys, Al-alloys, and steels often contain non-metallic inclusions in their microstructures. These inclusions, which include oxide particles, carbides, and intermetallic particles, are introduced during component manufacturing processes such as casting, powder-metallurgy, or additive manufacturing methods. The presence of inclusions in the microstructure can promote fatigue crack nucleation by competing against slipband nucleation and reduce fatigue life performance of an engineering component. While it has been reported in many occasions, the competition between fatigue crack nucleation at inclusions and slipbands is still not well understood. In this article, the conditions for the concurrent occurrence of fatigue crack nucleation at inclusions and slipbands are analyzed theoretically. The analysis indicates that there exists a critical inclusion size (diameter) below which there is no fatigue life debit due to crack initiation at inclusions and above which a transition from slip-induced to inclusion-induced crack nucleation occurs. The low-cycle fatigue life model is applied to Ni-based superalloys and the model predictions are compared against experimental data from the literature to assess the dependence of the critical inclusion size on the slip morphology, grain size of the matrix, and the shear modulus of the inclusion.

Microstructural damage sensitivity prediction using spatial statistics

The vast compositional space of metallic materials provides ample opportunity to design stronger, more ductile and cheaper alloys. However, the substantial complexity of deformation micro-mechanisms makes simulation-based prediction of microstructural performance exceedingly difficult. In absence of predictive tools, tedious experiments have to be conducted to screen properties. Here, we develop a purely empirical model to forecast microstructural performance in advance, bypassing these challenges. This is achieved by combining in situ deformation experiments with a novel methodology that utilizes n-point statistics and principle component analysis to extract key microstructural features. We demonstrate this approach by predicting crack nucleation in a complex dual-phase steel, achieving substantial predictive ability (84.8% of microstructures predicted to crack, actually crack), a substantial improvement upon the alternate simulation-based approaches. This significant accuracy illustrates the utility of this alternate approach and opens the door to a wide range of alloy design tools.

Microstructurally-sensitive fatigue crack nucleation in Ni-based single and oligo crystals

An integrated experimental, characterisation and computational crystal plasticity study of cyclic plastic beam loading has been carried out for nickel single crystal (CMSX4) and oligocrystal (MAR002) alloys in order to assess quantitatively the mechanistic drivers for fatigue crack nucleation.The experimentally validated modelling provides knowledge of key microstructural quantities (accumulated slip, stress and GND density) at experimentally observed fatigue crack nucleation sites and it is shown that while each of these quantities is potentially important in crack nucleation, none of them in its own right is sufficient to be predictive. However, the local (elastic) stored energy density, measured over a length scale determined by the density of SSDs and GNDs, has been shown to predict crack nucleation sites in the single and oligocrystals tests. In addition, once primary nucleated cracks develop and are represented in the crystal model using XFEM, the stored energy correctly identifies where secondary fatigue cracks are observed to nucleate in experiments. This (Griffith-Stroh type) quantity also correctly differentiates and explains intergranular and transgranular fatigue crack nucleation.

Identifying the crack path for the phase field approach to fracture with non-maximum suppression

The phase field method is proven to be a powerful tool in computational fracture mechanics in that it can predict crack nucleation and branching, in some cases, without explicitly tracking the crack path. However, in such applications as hydraulic fracturing or leakage, it is necessary or beneficial to have the crack geometry available. This paper presents a variational method to identify the crack path from phase field approaches to fracture. The method is proven to be successful not only for a simple curved crack but also for multiple and branched cracks. The algorithm employs the non-maximum suppression technique, a procedure borrowed from the image processing field, to detect a bounding area which covers the ridge of the phase field profile. After that, it is continued with the step to determine a cubic spline to represent the crack path and to improve it via a constrained optimization process. To demonstrate the performance of our method, we provide the results with three sets of representative examples.

Massive parallelization of the phase field formulation for crack propagation with time adaptivity

The phase field method has proven to be an important tool in computational fracture mechanics in that it does not require complicated crack tracking and is able to predict crack nucleation and branching. However, the computational cost of such a method is high due to a small regularization length parameter, which in turn restricts the maximum element size that can be used in a finite element mesh. In this work we developed a massively parallel algorithm on the graphical processing unit (GPU) to alleviate this difficulty in the case of dynamic brittle fracture. In particular, we adopted the standard finite element method on an unstructured mesh combined with second order explicit integrators. To ensure stability, we designed a time adaptivity strategy to account for the decreasing critical time step during the evolution of the fields. We demonstrated the performance of the GPU-implemented phase field models by means of representative numerical examples, with which we studied the effect of the artificial viscosity, an artificial parameter to be input, and compared the crack path branching predictions from three popular phase field models. Finally, we verified the method with convergence studies and performed a scalability study to demonstrate the desired linear scaling of the program in terms of the wall time per physical time as a function of the number of degrees of freedom.