Cracking Criterion Research Articles

Matrix cracking in polymer matrix composites under bi-axial loading

A model to predict the matrix crack evolution in a continuous fiber polymer composite laminate under in-plane bi-axial static loading has been presented in the current work. Oblique co-ordinate based shear lag analysis was used to estimate the stress distribution inside the cracked [0/90] s cross-ply T300/934 carbon fiber reinforced plastic (CFRP) laminate. Weibull probability distribution has been used to account for the variation in ply transverse strength. Size-dependent strength due to variation in ply thickness has been accounted for by appropriate volume scaling based Weibull scale factor. The Weibull parameters have been estimated using a ‘master laminate’ crack evolution data. By applying incremental stress to the laminate, using the probabilistic variation of transverse strength and the stress at a material point, the new crack location has been identified using the Hashin matrix cracking criterion. The reciprocal of the normal distance between two cracks has been termed as crack density. The crack density evolution for cross-ply laminates with an increase in applied loading has been estimated for various bi-axial ratios and compared with the data available from the literature. A good correlation is found to exist between the literature evolution data and current simulation predictions.

Formation Criterion of Hydrogen-Induced Cracking in Steel Based on Fracture Mechanics

A new criterion for hydrogen-induced cracking (HIC) that includes both the embrittlement effect and the loading effect of hydrogen was obtained theoretically. The surface cohesive energy and plastic deformation energy are reduced by hydrogen atoms at the interface; thus, the fracture toughness is reduced according to fracture mechanics theory. Both the pressure effect and the embrittlement effect mitigate the critical condition required for crack instability extension. During the crack instability expansion, the hydrogen in the material can be divided into two categories: hydrogen atoms surrounding the crack and hydrogen molecules in the crack cavity. The loading effect of hydrogen was verified by experiments, and the characterization methods for the stress intensity factor under hydrogen pressure in a linear elastic model and an elastoplastic model were analyzed using the finite-element simulation method. The hydrogen pressure due to the aggregation of hydrogen molecules inside the crack cavity regularly contributed to the stress intensity factor. The embrittlement of hydrogen was verified by electrolytic charging hydrogen experiments. According to the change in the atomic distribution during crack propagation in a molecular dynamics simulation, the transition from ductile to brittle fracture and the reduction in the fracture toughness were due to the formation of crack tip dislocation regions suppressed by hydrogen. The HIC formation mechanism is both the driving force of crack propagation due to the hydrogen gas pressure and the resisting force reduced by hydrogen atoms.

On the theoretical modeling of fatigue crack growth

Although fatigue is by far the most common mode of failure of structural materials, mechanistic understanding is still lacking. For example, the fundamental Paris law which relates the crack growth rate to stress-intensity factor range is still phenomenological and no reliable mechanistic model has been established for a given material or class of materials despite numerous investigations over a half a century. This work is an attempt to theoretically model fatigue crack propagation induced by alternating crack-tip plastic blunting and re-sharpening in the mid-range of growth rates on the basis of inputs from experiments that measure macroscopic material behavior, e.g., response to uniaxial cycling loading. In particular, we attempt to predict Paris law behavior by accounting for the material constitutive behavior in response to cyclic loading by modeling crack advance solely in terms of the underlying plastic dissipation. We obtain the steady-state condition for crack growth based on plastic dissipation, numerically using finite element analysis, which involves a methodology to address plastic closure upon unloading. For a given stress-intensity range, we calculate the crack propagation rate from the steady-state condition through each cycle of loading and unloading of a cracked compact-tension specimen, without resorting to any specific criterion for crack advance.

Stable and realistic crack pattern generation using a cracking node method

This paper presents a method for simulating surface crack patterns appearing in ceramic glaze, glass, wood and mud. It uses a physically and heuristically combined method to model this type of crack pattern. A stress field is defined heuristically over the triangle mesh of an object. Then, a first-order quasi-static cracking node method (CNM) is used to model deformation. A novel combined stress and energy combined crack criterion is employed to address crack initiation and propagation separately according to physics. Meanwhile, a highest-stress-first rule is applied in crack initiation, and a breadth-first rule is applied in crack propagation. Finally, a local stress relaxation step is employed to evolve the stress field and avoid shattering artifacts. Other related issues are also discussed, such as the elimination of quadrature sub-cells, the prevention of parallel cracks and spurious crack procession. Using this method, a variety of crack patterns observed in the real world can be reproduced by changing a set of parameters. Consequently, our method is robust because the computational mesh is independent of dynamic cracks and has no sliver elements. We evaluate the realism of our results by comparing them with photographs of real-world examples. Further, we demonstrate the controllability of our method by varying different parameters.

Lifetime prediction of filled elastomers based on particle distribution and the J-integral evaluation

This work presents the lifetime prediction of elastomer component based on the particle distribution in the specimen, the crack growth properties and the appropriate crack criterion. A lifetime prediction using numerical simulation saves both cost and time and can be very helpful in the development phase of a product. On the basis of the obtained results, lifetime can be estimated and thus an appropriate measure such as geometry change or load adjustment can be adopted. The prediction is demonstrated using two kinds of elastomer samples: EPDM and NR under different load amplitudes. Lifetime prediction is accomplished by Monte Carlo simulation, which is based on the correlation between the value of J-integral and total energy density of the single-edge notched tension (SENT) sample. Due to the choice of an inelastic material law the J-integral is evaluated after establishment of stable load cycles as the stable value for a J-integral contour curve as a function of the contour curve distance from the crack tip.For lifetime prediction, a Python script was implemented for the commercial FEA system Abaqus as a postprocessing routine. The script is based on local lifetime evaluation, where evaluation is done element by element followed up by an accumulation. In addition, physical experiments are used for counting the particles in the materials, to characterise the crack growth and also to measure lifetime.

3D multi-scale multi-physics modelling of hot cracking in welding

A 3D multi-scale and multi-physics numerical model has been developed and validated to predict the occurrence of hot cracking during fusion welding of Al-Mg-Si alloys. The new model consists of four modules: (I) a welding solidification module that creates the desired weld microstructure consisting of both columnar and equiaxed grains and varies as a function of welding conditions; (II) a thermo-mechanical analysis module that predicts the deformation of the weld mushy zone due to solidification contraction and the response of the base metal; (III) a fluid flow module that calculates the variation in fluid velocity and pressure within the micro liquid channels of the semisolid; and (IV) a crack initiation module that applies Kou's hot cracking criterion [1] to identify cracked liquid channels based on inputs from the solidification, thermo-mechanical and fluid-flow modules. The results identify the underlying mechanisms by which welding process parameters (current and travel speed) and external restraining conditions influence hot cracking susceptibility during Gas Tungsten Arc welding. Interestingly, micro hot cracks seem to initiate near the fusion zone but then localize and form a macroscopic hot crack at the core of the weld.

Coupled stress and energy criterion for multiple matrix cracking in cross-ply composite laminates

Transverse cracking, i.e. matrix cracking in the off-axis plies of the laminate, is widely recognized as the first damage mode to appear in continuous fibre-reinforced composite laminates subjected to in-plane loading. Since transverse cracking has a great influence on the subsequent damage steps such as delaminations or oblique cracks, it is important to be able to predict its onset and growth accurately. In this paper, it is proposed to use a combination of the Coupled Criterion of Finite Fracture Mechanics (FFM) and the Equivalent Constraint Model (ECM) to predict the evolution of crack density with increasing applied load. Two formulations – a discrete formulation and a continuous formulation – are developed for the energy criterion within the Coupled Criterion. Some dependences between the two formulations are proved, which justifies the good agreement found by the models based on continuous formulations presented by other authors despite the inherent discrete nature of the phenomenon. Dependence of the failure load predicted by the Coupled Criterion on the layer thickness ratio and brittleness number (a structural parameter that characterizes a combination of the stiffness, strength, fracture toughness and the thickness of the cracked ply of the laminate) is examined and discussed for carbon/epoxy and glass/epoxy laminates. Finally, a comparison against experimental results shows a good agreement.

Hot Cracking Mechanisms in Welding Metallurgy: A Review of Theoretical Approaches

Hot cracking often refers to the appearance of liquid films along grain boundaries or to another place in the weld metal structure. Despite hot cracking importance in alloy weldability, there is limited understanding of the influencing mechanisms. Theories and criteria worked out over the years to assess alloy weldability will be presented. The review focuses on: 1) Theories of hot cracking, 2) Hot cracking criteria, and 3) A criticism of hot cracking theories and criteria.

Predictions of fracture load, crack initiation angle, and trajectory for V-notched Brazilian disk specimens under mixed mode I/II loading with negative mode I contributions

In this paper, first the fracture load, the crack initiation angle and the crack trajectory are experimentally measured for the round-tip V-notched Brazilian disk specimen made of polymethyl-methacrylate under compressive-shear loading. Then, the fracture load and the crack initiation angle are predicted by using the extended finite element method on the basis of the linear cohesive crack criterion. The fracture trajectory of the round-tip V-notched Brazilian disk specimens is also estimated by means of the extended finite element method and the incremental methods. Both the experimental observations and the theoretical fracture models indicate that although the notch bisector line is under compressive-shear loading, one half of the notch border still sustains tensile stresses and fracture takes place from this half. A very good agreement is shown to exist between the theoretical predictions and the experimental results for various notch opening angles and different notch radii.

Mechanical properties and cold cracking evaluations of four 7××× series aluminum alloys using a newly developed index

Cold cracking is a severe challenge during the direct-chill casting of high-strength 7××× series aluminum alloys. A finite element method (FEM) simulation combined with a cold cracking criterion has been demonstrated to possess obvious technical advantages in cold cracking prediction. However, the current absence of mechanical properties and effective criteria for 7××× series aluminum alloys inhibits the progress of the technique. In this study, the corresponding mechanical properties of four typical 7××× series aluminum alloys are investigated. The cold cracking tendencies of the alloys are evaluated by a new cold cracking index (CCI) developed by the authors. It is shown that AA7055 has the highest cold cracking propensity among the four alloys, followed by AA7050, AA7085, and AA7022, respectively. The cold cracking tendency is basically consistent with the amount of nonequilibrium eutectics of the alloys under the same casting process. It is also shown that the application of water wiper can effectively decrease the occurrence of cold cracking.

A peridynamics formulation for quasi-static fracture and contact in rock

We present a dual-horizon peridynamics (DH-PD) formulation for fracture in granular and rock-like materials. In contrast to discrete crack methods such as XFEM, DH-PD does not require any representation of the crack surface and criteria to treat complex fracture patterns such as crack branching and coalescence. The crack path is the natural outcome of the simulation. In this manuscript, a new penalty method to model the contact for compressive fractures and constraining the penetration conditions is developed. The new method is applied to several benchmark problems in geomechanics including the four-point shear test, the indirect tensile (Brazilian) test of rock disks with one or multiple initial cracks. By using an appropriate damping coefficient, the quasi-static solution for rock failure is obtained when the dynamic formulation is used. A good agreement is obtained between the results given by DH-PD and those by the experiments.

Statistical evolution of short fatigue crack growth rate for LZ50 axle steel

Initiation and propagation of short fatigue crack occupy most of the fatigue life of metal components with smooth surface. To characterize the statistical evolution behavior of short fatigue crack growth, totally 9 hourglass shaped specimens were fatigued under a loading frequency of 15 Hz by short fatigue crack replica test method. Afterwards, according to the “effective short fatigue crack criterion”, replica test results were observed. Growth rate of DESFC for all specimens were obtained and analyzed. Combined with metallurgical test of LZ50 axle steel, conclusions can be drawn that it is the restraints of ferrite grain boundary and rich pearlite banded structure that cause the twice decline of DESFC growth rate. DESFC growth rates of each specimen at 10 given crack lengths and fatigue life fractions were obtained using linear interpolation method. The dispersion of DESFC growth rates was large and not steady in early cycles of MSC stage. But with the increase of loading cycles, the overall dispersion come down in later cycles of PSC stage gradually. Furthermore, seven commonly used distributions, i.e., 3PWD, 2PWD, ND, LND, EMVD1, EMVD2 and ED, were compared on three aspects, i.e., total fitting effect, consistency with the relevant fatigue physics, and safety of design evaluation. The results show that the ND, instead of 3PWD and 2PWD, is a good distribution for the growth rates of DESFC.DOI: http://dx.doi.org/10.5755/j01.mech.23.2.18108

Different Techniques of Determination of the Cracking Criterion for Solidification in Casting

Cracking which occurs during the solidification process is a serious defect in castings and welds. Alloys are susceptible to cracking during solidification. Al alloys, stainless steels and Ni-base alloys are notable examples. Cracking takes place in the semisolid region called the mushy zone. During solidification, shrinkage and thermal contraction of the mushy zone and its surrounding solid are hindered, tensile deformation can induce cracking (in the semisolid region) along grain boundaries that are not fed with sufficient liquid phase. The cracking criterion is focused on events occurring at the grain boundary, including separation of grains from each other, lateral growth of grains toward each other, and liquid feeding between grains. The susceptibility factor of a binary aluminum alloy to cracking during solidification was also described. The criterion has an effect upon: (a) the lateral growth rate of two neighboring grains toward each other to bond together to resist cracking, and (b) the length of the grain-boundary liquid channel through which feeding has to occur to resist cracking. In future work the criterion will be compared with experimental data and computer simulation during solidification of binary aluminum alloys in welding.

Investigation for plastic damage constitutive models of the concrete material

In this paper, some simple stress-strain relationships of the concrete material recommended in relevant Codes are appropriately simplified, then the damage factors of the simplified plastic damage constitutive model is determined based on Sidiroff’s energy equivalence principle. Mechanical characteristics of the concrete material under the simple tension or compression are analyzed by Finite element method. Through the comparison of numerical analysis results and Code constitutive relations, the damage factors of the simplified plastic damage constitutive model is verified. The unreinforced concrete beam static tests by Petersson is simulation analyzed by the nonlinear finite element method and plastic damage constitutive model. The effect of the unit size and the different linear softening constitutive relation on the analysis results are considered. The results show that there is no obvious size effect on the plastic damage analysis results based on fracture cracking criterion, the results of the bilinear softening constitutive analysis have good accuracy, and the form of softening constitutive relation has a great influence on the result.

Mesoscopic analysis of Crack Propagation in Concrete by Nonlinear Finite Element Method with Crack Queuing Algorithm

By means of nonlinear finite element method, the initiation and propagation of cracks in concrete are analysed numerically at the mesoscopic level. The concrete is treated and modelled as a three-phase system consisting of coarse aggregate, hardened mortar matrix and interfacial transition zones between coarse aggregate and mortar matrix. Nonlinear constitutive properties of the materials before and after cracking are incorporated in the modelling. An integrated cracking criterion based on both tensile strength and fracture toughness is proposed to cater for stress concentration at crack tips, and a crack queuing algorithm is employed to simulate the stress redistribution and stress relief upon cracking. To illustrate the applications of the proposed method, an example of the cracking process of concrete is presented.

Use of Indicators for Hot and Warm Cracking in Welded Structures

Weight reduction of mechanical components is becoming increasingly important as a way to provide more environment friendly production and operation of different equipment. This is true in almost any manufacturing industry, but is especially important to the aerospace industry. Casting has often been replaced by hot and cold metal working operations and welding, usually including an additional heat treatment. This gives components better material properties and provides components with less weight and cost but with increased strength and efficiency. This may even be true for rotating Ni- based superalloy components, and is enabled by welding methods. However, weld cracking of precipitation hardening Ni-based superalloys is a serious problem, both in manufacturing and overhaul since it endangers component life if cracks are allowed to propagate.Cracks can appear in a weld and in it's surroundings. The triggering mechanisms depend on its location and when it is nucleated. Generally saying, weld cracking in precipitation hardening Ni-based superalloys consists of two different types of cracking, hot cracking and warm cracking which may be further divided into heat affected zone (HAZ) liquation cracking, solidification cracking and strain age cracking, respectively.Finite element simulations of welding and heat treatment processes started in the seventies for small laboratory set-up cases and have today matured, and are now used on large-scale structures like aerospace components. But FE-based crack criteria that can predict the risk of cracking due to welding or heat treatments are rare. In a recent study both hot cracking and warm cracking have been investigated in Ni-based superalloys, and two FE-based indicators showing the risk of hot and warm cracks have been proposed. The objective of the investigation presented in this paper is to compare results from FE-simulations with experimental results from weldability tests, like the Varestraint test and the high temperature mechanical Gleeble test.

A Statistics-Based Cracking Criterion of Resin-Bonded Silica Sand for Casting Process Simulation

Cracking of sand molds/cores can result in many casting defects such as veining. A robust cracking criterion is needed in casting process simulation for predicting/controlling such defects. A cracking probability map, relating to fracture stress and effective volume, was proposed for resin-bonded silica sand based on Weibull statistics. Three-point bending test results of sand samples were used to generate the cracking map and set up a safety line for cracking criterion. Tensile test results confirmed the accuracy of the safety line for cracking prediction. A laboratory casting experiment was designed and carried out to predict cracking of a cup mold during aluminum casting. The stress–strain behavior and the effective volume of the cup molds were calculated using a finite element analysis code ProCAST®. Furthermore, an energy dispersive spectroscopy fractographic examination of the sand samples confirmed the binder cracking in resin-bonded silica sand.

Coupled domain decomposition–proper orthogonal decomposition methods for the simulation of quasi-brittle fracture processes

In this paper, we discuss a strategy to reduce the computational costs of the simulation of dynamic fracture processes in quasi-brittle materials, based on a combination of domain decomposition (DD) and model order reduction (MOR) techniques. Fracture processes are simulated by means of three-dimensional finite element models in which use is made of cohesive elements, introduced on-the-fly wherever a cracking criterion is attained. The body is initially subdivided into sub-domains; for each sub-domain MOR is obtained through a proper orthogonal decomposition (POD) of the equations governing its evolution, until when it starts getting cracked. After crack inception within a sub-domain, the solution is switched back to the original full-order model for that sub-domain only. The computational gain attained through the coupled use of DD and POD thus depends on the geometry of the body, on the topology of sub-domains and, on top of all, on the spreading of cracking induced by load conditions. Numerical examples concerning well-established fracture tests are used for validation, and the attainable reduction of the computing time is discussed at varying decomposition into sub-domains, even in the absence of a full exploitation of parallel computing potentialities.

Influence of external loads on a characteristic angle between grains and solidus line as an indicator for hot cracking susceptibility during GTA welding

A long list of criteria determining the hot cracking susceptibility already exists. A main influence on solidification cracking can result from the design of the welded construction, i.e. from the influence of external loads. Using the Controlled Tensile Weldability (CTW) test, an external load hot cracking test, the influence of constant pre-load and different extension rates on the solidification cracking behavior of GTA (Gas Tungsten Arc) welds in an austenitic (AISI 309) and a ferritic (AISI 441) steel were investigated. Compared to specimens welded allowing free shrinkage and welded with an applied constant tensile pre-load, the specimens welded during the application of increasing tensile load show solidification cracks. In the weld seams, a characteristic angle α between the predominantly columnar grains and the fusion line can be observed. Specimens showing solidification cracks show a significantly larger angle α compared to the crack-free specimens. Based on these observations, the characteristic angle α is proposed as a new hot cracking criterion.

An investigation of ductility-dip cracking in the base metal heat-affected zone of wrought nickel base alloys—part II: correlation of PVR and STF results

Ductility-dip cracking (DDC) in the base metal heat-affected zone (HAZ) of NiCr15Fe-type alloys was studied using the programmable-deformation-crack (PVR) and the strain-to-fracture (STF) test. This paper concentrates on the correlation of the different cracking criteria used in both tests for DDC susceptibility assessment. Full temperature-strain curves were developed for three base metal NiCr15Fe-alloy variants using the STF test. The results were compared to a previous material ranking obtained by PVR testing. To determine a local cracking criterion for base metal DDC in the PVR test, a finite element analysis (FEM) was conducted on the thermomechanical aspects of crack initiation during PVR testing. The local temperature and strain conditions associated with DDC in the PVR base metal HAZ were observed and discussed with regard to the comparability and transferability of the cracking criteria used in the PVR and STF test.