Crack Propagation In Materials Research Articles

Efficient BFGS quasi-Newton method for large deformation phase-field modeling of fracture in hyperelastic materials

The prediction of crack propagation in materials is a crucial problem in solid mechanics, with many practical applications ranging from structural integrity assessment to the design of advanced materials. The phase-field method has emerged as a powerful tool for modeling crack propagation in materials, due to its ability to accurately capture the propagation of cracks. However, current phase-field algorithms suffer from the elevated computational cost associated with the so-called staggered solution scheme, which requires extremely small time increments to advance the crack due to its inherent conditional stability. In this paper, we present, for the first time, a quantitative analysis detailing the numerical implementation and comparison of two common solution strategies for the coupled large-deformation solid-mechanics-phase-field problem, namely the quasi-Newton based Broyden–Fletcher–Goldfarb–Shanno algorithm (BFGS) and the full Newton based alternating minimization (or staggered) (AM/staggered) algorithm. We demonstrate that the BFGS algorithm is a more efficient and advantageous alternative to the traditional AM/staggered approach for solving coupled large-deformation solid-mechanics-phase-field problems. Our results highlight the potential of the quasi-Newton BFGS algorithm to significantly reduce the computational cost of predicting crack propagation in hyperelastic materials while maintaining the accuracy and robustness of the phase-field method.

The Review of Research on Fatigue Crack Propagation in Metallic Materials

In recent years, with the development of industry and scientific technology, the demand for materials has been increasing. Fatigue crack propagation is an important issue in the field of materials, and developing relevant theories and methods, understanding the mechanisms of fatigue cracks, and making scientific predictions on fatigue crack propagation are hot topics both domestically and internationally. Fracture mechanics, as a discipline studying the strength and propagation of cracks in materials, has developed a relatively complete theoretical system and engineering application methods over more than 100 years of continuous development. This article focuses on the effects of factors such as temperature, stress ratio, and load frequency on the fatigue crack propagation characteristics of metallic materials, and summarizes the common theories and methods of fatigue crack propagation.

The displacement mechanism of the cracked rock – a seismic design and prediction study using XFEM and ANNs

Materials with sufficient strength and stiffness can transfer nonlinear design loads without damage. The present study compares crack propagation speed and shape in rock-like material and sandstone when subjected to seismic acceleration. The nonlinear extended finite element method (NXFEM) has been used in numerical simulation. It assumes the model has a pre-existing crack at 0° from the horizontal. The mechanical properties of the model, crack propagation shape, and crack speed were selected as the main parameters. The nonlinear stress and strain along the crack have been compared in two simulated models. NXFEM and Artificial Neural Networks (ANNs) were used to predict the displacement. The simulation results illustrate that the materials’ crack propagation mechanism and mechanical properties control the stress, strain, and displacement at the selected points in the model. In addition, crack propagation in materials is related to elastic-plastic stresses and strains along the crack path. The speed and shape of the crack are associated with the mechanical properties of the materials. The prediction of crack paths helps to understand failure patterns. Comparison of the seismic response of the rock-like material with sandstone helps to assess the stress, strain, and displacement levels during cracking. This study’s findings agree with the literature report and field observations.

Interaction of cracks with grain boundaries in iron bicrystals

Molecular dynamic modelling of seed cracks evolution in iron bicrystals with inclined grain boundaries under uniaxial expansion was carried out. The process of seed crack evolution can be divided into four stages. At the first stage, in the interval of elastic deformations, the seed crack is stationary, and the stresses increase linearly, reaching a maximum value of ~7.0 GPa. At the same time, the atomic volume and stresses at the crack tip before its opening grow significantly faster than the average for the sample. At the second stage, the crack begins to spread into the grain volume. The process of crack propagation leads to an abrupt stress release due to relaxation processes in the areas adjacent to the crack banks and the emission of defects from the crack tip. After reaching the grain boundary, the crack stops and blunts. At the third stage, the crack remains in the grain boundary, and the sample stresses experience significant oscillations, which is caused by the emission of various defects both from the grain boundary and from other interfaces. The emission of defects from the crack tip can cause local migration of the grain boundary, which is formation of a bend on the initially flat surface of the grain boundary. When defects cease to be emitted from the crack tip, the voltage and atomic volume in this region increase rapidly. At the fourth stage, the crack begins to spread into the second grain. It was found that a boundary with a large grain misorientation angle is a more effective barrier restraining crack propagation. Initiation of the seed crack propagation in material is always preceded by an abrupt increase in atomic volume and stresses at the crack tip.

Experimental and Analytical Investigation of Fracture Characteristics of Steel Fiber-Reinforced Recycled Aggregate Concrete

AbstractFracture parameters of fiber concrete (FC) are currently a hot research area. Fracture mechanics is the field of solid mechanics that helps to study the type and propagation of cracks in materials. It uses methods of calculating the driving force on a crack and characterizes the material's resistance to fracture. Behavioral characteristics are determined by crack mouth opening displacement and the load–deflection method. This research identifies the fracture parameters of 33 notched simply supported beams made by recycled aggregate cement concrete with steel fiber. The recycled aggregate ratio in concrete has been altered to determine the effect on the mechanical and fracture properties. For determining fracture parameters, a 3-point bending single-edge notched fracture test was used. The results indicated that the steel fiber-reinforced concrete made with recycled aggregate showed similar performance and fracture characteristics compared to normal concrete. Thus, adding steel fibers to various concrete mixes considerably improved the fracture characteristics, while the brittleness was reduced with increased steel fiber content. Linear regression analysis also showed the accuracy of mechanical strength results as the value of R-square was close to unity. Displacement, ultimate load, brittleness (B), fracture toughness (KIC), crack mouth opening displacement (CMOD), fracture energy (GF), modulus of elasticity (E), and characteristic length (lch), were determined for both conventional and recycled aggregate specimens. The “work of fracture"—by definition the formula—is the most reliable to calculate the fracture energy as the nonlinearity is related to the performance of FC.

Comparative Analysis of Machine Learning Models for Predicting Crack Propagation under Coupled Load and Temperature

Crack propagation in materials is a complex phenomenon that is influenced by various factors, including dynamic load and temperature. In this study, we investigated the performance of different machine learning models for predicting crack propagation in three types of materials: composite, metal, and polymer. For composite materials, we used Random Forest Regressor, Support Vector Regression, and Gradient Boosting Regressor models, while for polymer and metal materials, we used Ridge, Lasso, and K-Nearest Neighbors models. We trained and tested these models using experimental data obtained from crack propagation tests performed under varying load and temperature conditions. We evaluated the performance of each model using the mean squared error (MSE) metric. Our results showed that the best-performing model for composite materials was Gradient Boosting Regressor, while for polymer and metal materials, Ridge and K-Nearest Neighbors models outperformed the other models. We also validated the models using additional experimental data and found that they could accurately predict crack propagation in all three materials with high accuracy. The study’s findings provide valuable insights into crack propagation behavior in different materials and offer practical applications in the design, construction, maintenance, and inspection of structures. By leveraging this knowledge, engineers and designers can make informed decisions to enhance the strength, reliability, and durability of structures, ensuring their long-term performance and safety.

Suitability Analysis of Machine Learning Algorithms for Crack Growth Prediction Based on Dynamic Response Data.

Machine learning has the potential to enhance damage detection and prediction in materials science. Machine learning also has the ability to produce highly reliable and accurate representations, which can improve the detection and prediction of damage compared to the traditional knowledge-based approaches. These approaches can be used for a wide range of applications, including material design; predicting material properties; identifying hidden relationships; and classifying microstructures, defects, and damage. However, researchers must carefully consider the appropriateness of various machine learning algorithms, based on the available data, material being studied, and desired knowledge outcomes. In addition, the interpretability of certain machine learning models can be a limitation in materials science, as it may be difficult to understand the reasoning behind predictions. This paper aims to make novel contributions to the field of material engineering by analyzing the compatibility of dynamic response data from various material structures with prominent machine learning approaches. The purpose of this is to help researchers choose models that are both effective and understandable, while also enhancing their understanding of the model's predictions. To achieve this, this paper analyzed the requirements and characteristics of commonly used machine learning algorithms for crack propagation in materials. This analysis assisted the authors in selecting machine learning algorithms (K nearest neighbor, Ridge, and Lasso regression) to evaluate the dynamic response of aluminum and ABS materials, using experimental data from previous studies to train the models. The results showed that natural frequency was the most significant predictor for ABS material, while temperature, natural frequency, and amplitude were the most important predictors for aluminum. Crack location along samples had no significant impact on either material. Future work could involve applying the discussed techniques to a wider range of materials under dynamic loading conditions.

Effect of Crack Length on Stresses in a Plate with a Hole

The field of mechanics concerned with studying the propagation of cracks in materials is Fracture Mechanics. Technology systems are meant to withstand the loads to which they are likely to be exposed when in use. Material imperfections arising at the time of production or use of the material are, however, unavoidable and must therefore be taken into account. A stress intensity factor is a fracture parameter that defines the part failure. This paper study’s the effect of cracks on the stresses of rectangular plates having a hole in the center. The plate was subjected to tensile pressure at the top side while maintaining the bottom side fixed. The plate had four cracks distributed around the centered hole at 45o at each side. The effect of the length of the cracks on the resulted stresses and strains was investigated. Also, the effect of the position of the crack on the resulted stresses and strains was studied. Finite element models for the different plate cases were built using ANSYS software. The results showed that increasing the crack length resulted to increase the stresses and strains. The dimension of the plate width, height and thickness were 150 mm, 300 mm and 1 mm respectively, and the crack position was investigated for different crack lengths (5, 10, 15, 20, 25 mm) however the results were not steady as it looks that the crack lengths have changed the stress distribution over the plate.

Phase Field Models for Thermal Fracturing and Their Variational Structures.

It is often observed that thermal stress enhances crack propagation in materials, and, conversely, crack propagation can contribute to temperature shifts in materials. In this study, we first consider the thermoelasticity model proposed by M. A. Biot and study its energy dissipation property. The Biot thermoelasticity model takes into account the following effects. Thermal expansion and contraction are caused by temperature changes, and, conversely, temperatures decrease in expanding areas but increase in contracting areas. In addition, we examine its thermomechanical properties through several numerical examples and observe that the stress near a singular point is enhanced by the thermoelastic effect. In the second part, we propose two crack propagation models under thermal stress by coupling a phase field model for crack propagation and the Biot thermoelasticity model and show their variational structures. In our numerical experiments, we investigate how thermal coupling affects the crack speed and shape. In particular, we observe that the lowest temperature appears near the crack tip, and the crack propagation is accelerated by the enhanced thermal stress.

CIPFAR: A 3D unified numerical framework for the modeling of ductile fracture based on the phase field model and adaptive remeshing

In this paper, a general numerical framework for the modeling of ductile fracture in 3D meshes is introduced. The strategy is inspired from the phase field model and adaptive remeshing tools. The phase field model was introduced as a continuous model for predicting the initiation and propagation of cracks in materials. However, the model has a limitation on the choice of the characteristic length scale that controls the width of the cracked region. This work contributes to the full modeling of transition between the continuous damage using the phase field model to the discontinuous crack initiation and propagation within a unified numerical framework called CIPFAR. The contributions of the work include: (i). identification of the crack surface on arbitrary mesh topologies; (ii). intersection by a Sequence Agnostic Partitioning strategy which is introduced to adapt the mesh to the computed crack surface; (iii). a nodal duplication by virtual non-manifold patch repair to open the mesh. Combining all the mentioned algorithms with adaptive remeshing allows modeling the initiation and propagation of cracks in materials efficiently. Different numerical examples are presented to prove the ability of the developed algorithm to model ductile fracture cases without the need to predefine the crack initiation region.

Numerical integration in G/XFEM analysis of 2-D fracture mechanics problems for physically nonlinear material and cohesive crack propagation

PurposeThe aim of this paper is to present a novel data transfer technique to simulate, by G/XFEM, a cohesive crack propagation coupled with a smeared damage model. The efficiency of this technique is evaluated in terms of processing time, number of Newton–Raphson iterations and accuracy of structural response.Design/methodology/approachThe cohesive crack is represented by the G/XFEM enrichment strategy. The elements crossed by the crack are divided into triangular cells. The smeared crack model is used to describe the material behavior. In the nonlinear solution of the problem, state variables associated with the original numerical integration points need to be transferred to new points created with the triangular subdivision. A nonlocal strategy is tailored to transfer the scalar and tensor variables of the constitutive model. The performance of this technique is numerically evaluated.FindingsWhen compared with standard Gauss quadrature integration scheme, the proposed strategy may deliver a slightly superior computational efficiency in terms of processing time. The weighting function parameter used in the nonlocal transfer strategy plays an important role. The equilibrium state in the interactive-incremental solution process is not severely penalized and is readily recovered. The advantages of such proposed technique tend to be even more pronounced in more complex and finer meshes.Originality/valueThis work presents a novel data transfer technique based on the ideas of the nonlocal formulation of the state variables and specially tailored to the simulation of cohesive crack propagation in materials governed by the smeared crack constitutive model.

Fracture analysis of plates and shells using FEM and XFEM

Fracture mechanics is the field of mechanics concerned with the study of propagation of cracks in materials and recognizes the role of cracks in the performance of structures leading to damage tolerant design approach. Cracks or crack like defects is observed in many structures which may lead to their catastrophic failure under a tensile stress field. In this paper, the structural integrity of plates with surface and embedded cracks is investigated using ABAQUS FEA code and the fracture parameter—stress intensity factor (SIF)—is evaluated. Convergence study is conducted to arrive at the optimum mesh parameters using both the conventional finite element method and the extended finite element method (XFEM). The FE model is validated by comparing FE results with published numerical solutions. The effect of varying crack depth and location on SIF is studied. The FE results matched well with the closed-form solutions and experimental results. It is observed that the crack depth and its location have significant influence on SIF. The conventional finite element method requires a mesh that conforms to the crack geometry, typically with a very detailed, focused mesh at the crack tip. The crack front must be defined explicitly and must specify the virtual crack extension direction in addition to matching the mesh to the cracked geometry. XFEM gives better result for cylindrical shells without mesh refinement around crack tip.

An Improved Support Domain Model of Smoothed Particle Hydrodynamics Method to Simulate Crack Propagation in Materials

Smoothed particle hydrodynamics (SPH) has its unique advantages in simulating large deformation. However, in its calculation, it is easy for some regional particles to break off. This paper puts forward the concept of virtual crack boundary to solve crack propagating problems in the framework of SPH. The parameters of virtual crack boundary are determined by the projection method of descending dimension, which improves the support domains of crack tip particles. Based on the principle of minimum strain energy density factor in fracture mechanics, the initiation and extended directions of cracks in materials are estimated. By simulating the generation and expansion of three modes of cracks in materials, the SPH calculation results of the three types of support domain forms are compared with the ABAQUS simulation results and experiment results. It indicates that the method of virtual crack boundary method is more stable than the one based on discontinuous medium. And it can generate more reasonable results than the method based on continuous medium. This paper proves the effectiveness of strain energy density factor based on fracture mechanics theory in searching the direction of crack expansion using SPH, and explores the application of new support domain model in SPH crack solution.

Phase stability and mechanical properties of ternary transition elements X(X = Cu,Zn,Ag) in Al3Hf intermetallic from first-principles calculations

Site preference, phase stability and brittle vs ductile behaviors of ternary transition elements Cu, Zn and Ag in Al3Hf intermetallic are investigated by using of first-principles calculations. It is found that it has a phase transition from D023 phase to L12 phase for Al3Hf due to the strong Al site preference for Cu, Zn and Ag addition. It is shown that the role of activated antiphase boundaries on 〈110〉(001) plane is the key factor for the phase transition. Elasticity modulus show that ternary elements can effectively improve the ductility of Al3Hf due to the phase transition. Finally, cleavage fracture model and slip fracture model were used to give a prediction of brittle to ductile transition mechanism based on Griffith fracture theory. The energetic results show that the improved ductility is due to the activated dislocation emission but suppressed crack propagation in materials.

A novel micro-double cantilever beam (micro-DCB) test in an X-ray microscope to study crack propagation in materials and structures

High-resolution imaging of crack opening and propagation in 3D structures to study the fracture behaviour of materials requires new experimental setups. In this report, we describe a novel technique that provides in-situ 3D visualization of crack evolution with high resolution during mechanical loading of multi-component materials: a micro double cantilever beam (micro-DCB) test in an X-ray microscope. We demonstrate that crack opening and propagation can be visualized (in-situ) in the X-ray microscope with a spatial resolution of about 100 nm. For this experiment, micro-DCB samples were prepared to a thickness that was X-ray transparent in the direction normal to the crack front. During the micro-DCB experiment, the load is applied perpendicular to the optical axis of the X-ray microscope while images are collected with phase contrast imaging. The method is validated for a synthetic polymer, Nafion® (DuPont) with dispersed platinum particles.The proof-of-concept experiment demonstrates that sub-micron cracks can be visualized non-destructively, and that the in-situ micro-DCB test allows to study crack opening and propagation in materials. The technique offers several benefits over existing methods and is applicable across a range of disciplines, including materials science (e.g. composites), microelectronics, and life sciences (e.g. tissue, bones).

Experimental and numerical investigation of mode II failure behavior evaluation using three point bend, end notched flexure test

In the present paper the primary task is the study involving calculation of elastic properties of the composite from the individual properties of the E-glass fiber (650 GSM) and the properties of resin LY 556 with Hardener HY951. The properties of varying volumetric ratio of fiber are obtained from calculation of the properties by using rule of mixtures. Experimentally validating the theoretical and numerical approaches by comparing the load-displacement response and crack paths observed in large scale bridged crack propagation in laminated fiber-reinforced composites specimens. An effort is being made to develop a numerical framework for cohesive crack propagation and demonstrating its effectiveness by simulating failure through crack propagation in materials with complex microstructure like fiber reinforced composites. Experimentally validating the theoretical and numerical approaches by comparing the load-displacement response and crack paths observed in large scale bridged crack propagation in laminated fiber-reinforced composites specimens.

Stochastic modelling of crack propagation in materials with random properties using isometric mapping for dimensionality reduction of nonlinear data sets

AbstractFractures tend to propagate along the least resistance paths, and homogeneous‐based models may not be able to reliably predict the true crack paths, as they are not capable of capturing nonlinearities and local damage induced by local inhomogeneity. This paper presents a stochastic numerical modelling framework for simulating fracturing in natural heterogeneous materials. Fracture propagation is modelled using Francfort and Marigo's variational theory, and randomness in the material properties is introduced by random field principle. A computational strategy on the basis of nonlinear dimensionality reduction framework is developed that maps domain of spatially variable properties of the materials to a low‐dimensional space. This strategy allows us to predict the most probable fracture patterns leading to failure by an optimisation algorithm. The reliability and performance of the developed methodology are examined through simulation of experimental case studies and comparison of predictions with measured data.

AE Monitoring of Hydrogen Embrittlement Crack in Maraging Steel

AE (Acoustic Emission) result from initiation and propagation of cracks in materials. Then AE monitoring can detect the micro cracks. Maraging steels witch have superior strength are used as structural materials. However, these have hydrogen embrittlement problem under humid air. Hydrogen embrittlement resistance of maraging steels is usually estimated by visual testing (VT) which checks whether rupture or not in laboratory. However the testing method is batch style testing. Then it is difficult to estimate the exact rupture time through VT. Then the AE monitoring applied to detect hydrogen embrittlement of maraging steel. Hydrogen embrittlement crack accelerated by a droplet of NaCl solution that was set on the center of the maraging steel thin plate. In this case, the droplet was too small to determine the hydrogen embrittlement crack through the electrochemistry method.AE sensor also set on the plate and detected AE signals.AE signals were classified as to amplitude, frequency, and wave form. AE event rate was also focused. The surface crack propagation was also recorded by digital camera. Crack growth was confirmed from the pictures. AE event counts separate 3 regions. At first region, AE event counts detect before surface cracks were able to be observed. In this region, cracks may initiate under the droplet. At Second region, AE event counts were constantly increased. In this region it was observed that increment by crack growth was constant by digital camera. It shows that means the second region was the crack growth stage. At third region, AE event rate was increased twice. The second crack growth was observed in digital camera images. Then AE event rate reflected the number of cracks. There was good relation between crack propagation and AE event rate. AE event rates were difference between types of steels. The other steel which has high hydrogen embrittlement resistance tend to have low AE events rate.

Modeling of crack propagation on a mesoscopic length scale

AbstractModeling of crack propagation in materials has long been a challenge in solid‐state physics and materials science. The phase‐field method is basically developed for modeling solidification processes and has now established as one of the tools for the description of crack propagation. The applied models are thermodynamically consistent and predict crack propagation in homogeneous materials under the consideration of different loading types, multiple physical fields, geometrical and physical nonlinearities. One of the open challenges is the modeling of crack propagation on a mesoscopic length scale in multiphase or multi‐grain systems. In this work, we summarize our preliminary work to get closer to the goal of describing crack propagation on a mesoscopic length scale. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Phase-field modeling of crack propagation in multiphase systems

Modeling of crack propagation in materials has long been a challenge in solid-state physics and materials science. The phase-field method has now established as one of the tools for the description of crack propagation. The applied models are thermodynamically consistent and predict crack propagation in homogeneous materials under the consideration of different loading types, multiple physical fields and geometrical nonlinearities. Even dynamic loading processes are studied, including plastic effects. A multiphase-field model for crack propagation, which is indispensable to describe crack propagation on a mesoscopic length scale, is still missing. In this work, we overcome this deficiency and combine a crack propagation approach, which is based on Griffith’s theory, with an established multiphase-field model for phase transformation.