Experiment and Simulation of Breakage of Particle Compounds under Compressive Loading

Two-dimensional finite element (FE) compressive stress analyses were carried out on the particle compound material to understand the stress pattern distributions before cracking. FE analysis was followed by discrete element (DE) simulation. A study of the crack propagating mechanism in a particle was represented by a model material that typifies pellets of high-strength pressed agglomerate building materials. For this, concrete spheres of strength category B35 (compressive strength 35 N/mm²) were used. It was observed that the ring tensile stress is responsible for the crack initiation in the spherical particle compounds.     

DEM simulation of diametrical compression test on particle compounds

A 2 Dimensional discrete element analysis is carried out with diametrical stressing condition to understand the fracture behaviour of particle compounds. The new surface generation and particle size distributions are also analysed to study an efficiency of the crushing system. Concrete spheres of 150 mm diameter with properties of B35 (35 N/mm² compressive strength) are chosen to represent particle compounds. The paper discusses the discrete element approach for crack propagation analysis and their correlations in particle compounds.     

Prediction of solid block masonry prism compressive strength using FE model

Masonry strength is dependent upon characteristics of the masonry unit, the mortar and the bond between them. Empirical formulae as well as analytical and finite element (FE) models have been developed to predict structural behaviour of masonry. This paper is focused on developing a three dimensional non-linear FE model based on micro-modelling approach to predict masonry prism compressive strength and crack pattern. The proposed FE model uses multi-linear stress–strain relationships to model the non-linear behaviour of solid masonry unit and the mortar. Willam–Warnke’s five parameter failure theory developed for modelling the tri-axial behaviour of concrete has been adopted to model the failure of masonry materials. The post failure regime has been modelled by applying orthotropic constitutive equations based on the smeared crack approach. Compressive strength of the masonry prism predicted by the proposed FE model has been compared with experimental values as well as the values predicted by other failure theories and Eurocode formula. The crack pattern predicted by the FE model shows vertical splitting cracks in the prism. The FE model predicts the ultimate failure compressive stress close to 85% of the mean experimental compressive strength value.     

On the role of stress waves in dynamic rupture of cylindrical tubes

A systematic experimental/computational study was performed to investigate the role of stress waves in ductile fracture of cylindrical tubes. The stress waves were created by high‐speed moving load, which was produced by detonation of explosive cord inside two intact and two pre‐flawed steel tubes. Several distinct phenomena like cyclic crack growths in Modes I and III, crack flap bulging and crack curving/branching were observed and simulated by finite element (FE) method. The FE models were composed of 3D brick elements equipped with interface cohesive elements. The analysis results showed that the crack growths in Modes I and III were governed by the detonation‐induced stress waves. The crack speeds were obtained based on the increments of cyclic crack growth and the time period of the stress waves. The estimated crack speed range was 63–230 m s^?1 for the axial growth, whereas the average speed for growth in Mode III was 100 m s^?1.     

An Assessment of the C* and KI Parameters for Predicting Creep Crack Growth in a Ni-Base Superalloy (Waspaloy) at 700^C

The results of experimental creep crack growth tests, using compact tension specimens, made from a Ni-base superalloy (Waspaloy) at 700^{^}C are presented. The experimental results indicate that the creep crack growth rate data for the Ni-base superalloy Waspaloy, at 700^{^}C, can be correlated using the C^* parameter, calculated from load-line displacement rates. The mode-I stress intensity factor, K_I, does not appear to be capable of correlating the data except at high creep crack propagation rates. Analytical solutions indicate that creep crack growth was occurring under transient creep conditions in the experiments. Finite element (FE) simulations were performed in which the experimentally determined crack growth versus time results were imposed. The good agreement between the resulting FE solutions for load-line displacements and corresponding C^* values with the experimental results show that the FE simulation was successful. The FE simulation revealed that the creep zone increases as the crack growth and a transient state of creep occurs in the vicinity of the advancing crack tip. An apparent correlation between the crack growth rates and the C^* parameter has been shown. This information is helpful in assessing the likely usefulness of the C^* and K_I parameters for predicting creep crack growth in more general situations. This revised version was published online in August 2006 with corrections to the Cover Date.     

Strengthening of thin-webbed castellated beam using CFRP

Abstract

The utilisation of fibre reinforced polymers (FRP) in the rehabilitation of steel structures increased in recent years. This article presents the advantages of using carbon fibre reinforced polymers (CFRP) in strengthening of the thin-webbed castellated beam (TCB). The performances of CFRP strengthened TCBs were analysed using finite element (FE) tool ABAQUS^®. Nonlinear FE analysis was carried out to find the optimum geometrical. Nine different designations of TCBs were arrived based on weld lengths, perforation sizes and strengthening technique (three each). Though all three techniques increased the strength considerably, the third one had much greater efficiency and was more suitable.     

Creep crack growth simulations in 316H stainless steel

Virtual methods of predicting creep crack growth (CCG), using finite element analysis (FE), are implemented in a compact tension specimen, C(T). The material examined is an austenitic type 316H stainless steel at 550 °C, which exhibits power-law creep–ductile behaviour. A local damage-based approach is used to predict crack propagation and the CCG rate data are correlated with the C^∗ parameter. Two-dimensional elastic–plastic–creep analyses are performed under plane stress and plane strain conditions. Finite element CCG rate predictions are compared to experimental data and to the NSW and modified NSW (NSW–MOD) CCG models’ solutions, which are based on ductility exhaustion arguments. An alternative version of the NSW–MOD model is presented for direct comparison with the FE implementation. The FE predictions are found to be in agreement with the appropriate analytical solutions, and follow the trends of the experimental data at high C^∗ values. Accelerated cracking behaviour is observed experimentally at low C^∗ values, which is consistent with the standard plane strain NSW–MOD prediction. The FE model may be developed to predict this accelerated cracking at low C^∗ values so that the trends between CCG rates at high and low C^∗ values may be determined.     

The peak stress method applied to fatigue assessments of steel and aluminium fillet-welded joints subjected to mode I loading

The aim of this work is to present an engineering method based on linear elastic finite element (FE) analyses oriented to fatigue strength assessments of fillet‐welded joints made of steel or aluminium alloys and subjected to mode I loading in the weld toe region where fatigue cracks nucleate. The proposed approach combines the robustness of the notch stress intensity factor approach with the simplicity of the so‐called ‘peak stress method’. Fatigue strength assessments are performed on the basis of (i) a well‐defined elastic peak stress evaluated by FE analyses at the crack initiation point (design stress) and (ii) a unified scatter band (design fatigue curve) dependent on the class of material, i.e. structural steel or aluminium alloys. The elastic peak stress is calculated by using rather coarse meshes with a fixed FE size. A simple rule to calculate the elastic peak stress is also provided if a FE size different from that used in the present work is adopted. The method can be applied to joints having complex geometry by adopting a two‐step analysis procedure that involves standard finite element (FE) models like those usually adopted in an industrial context. The proposed approach is validated against a number of fatigue data published in the literature.     

Experimental and numerical investigations on fatigue behavior of aluminum alloy 7050-T7451 single lap four-bolted joints

The fatigue behavior of aluminum alloy 7050-T7451 single lap four-bolted joints was studied by high-frequency fatigue test and finite element (FE) methods. The fatigue test results showed that a better enhancement of fatigue life was achieved for the joints with high-locked bolts by employing the combinations of cold expansion, interference fit, and clamping force. The fractography revealed that fatigue cracks propagated tortuously; more fatigue micro-cliffs, tearing ridges, lamellar structure were observed, and fatigue striation spacing was simultaneously reduced. The evaluation of residual stress conducted by FE methods confirmed the experimental results and locations of fatigue crack initiation. The extension of fatigue lives can be attributed to the evolution of fatigue damage and effect of beneficial compressive residual stresses around the hole, resulting in the delay of crack initiation, crack deflection, and plasticity-induced crack closure.     

Fatigue crack growth in residual stress fields

A fatigue crack growth (FCG) model for specimens with well-characterized residual stress fields has been studied using experimental analysis and finite element (FE) modeling. The residual stress field was obtained using four point bending tests performed on 7050-T7451 aluminum alloy rectangular specimens and consecutively modeled using the FE method. The experimentally obtained residual stress fields were characterized using a digital image correlation technique and a slitting method, and a good agreement between the experimental residual stress fields and the stress field in the FE model was obtained. The FE FCG models were developed using a linear elastic model, a linear elastic model with crack closure and an elastic–plastic model with crack closure. The crack growth in the FE FCG model was predicted using Paris–Erdogan data obtained from the residual stress free samples, using the Harter T-method for interpolating between different baseline crack growth curves, and using the effective stress intensity factor range and stress ratio. The elastic–plastic model with crack closure effects provides results close to the experimental data for the FCG with positive applied stress ratios reproducing the FCG deceleration in the compressive zone of the residual stress field. However, in the case of a negative stress ratio all models with crack closure effects strongly underestimate the FCG rates, in which case a linear elastic model provides the best fit with the experimental data. The results demonstrate that the negative part of the stress cycle with a fully closed crack contributes to the driving force for the FCG and thus should be accounted for in the fatigue life estimates.     

Torsional and compression loading of paperboard packages: Experimental and FE analysis

The present study investigates torsional and compressive loading of a paperboard package. Finite element (FE) analyses simulating the tests were performed to improve understanding of the stresses and deformations in the paperboard during loading. A simple experimental characterization of the necessary material properties could be performed to represent the multi-ply paperboard as a single-ply structure. The results from the single-ply model were compared with a laminate model, and the differences between the models were small. Comparing experimental and FE simulations of box compression and torsion showed that the FE models could accurately predict the response curves. However, in the simulations, there was an overprediction of the maximum compressive force and maximum torque, which was expected since geometrical imperfections and the heterogeneous internal structure of the material were not accounted for in the material model or the FE model. Local yield lines formed at the onset of non-linearities in the package load–displacement curves. Therefore, the strength of the paperboard affects the maximum compressive strength and maximum torque, and the bending stiffness of the paperboard only had a minor effect. When a first local maximum was reached, the number of FE that reached the failure stress increased exponentially. The simulations also showed that box compression was not an effect of package height, but higher packages had a lower maximum torque.     

Effects of soft hemispherical particle on local surface stress of hard matrix

Abstract

Finite element analysis was performed to investigate the stresses within and around a soft hemispherical particle located on the surface of a hard matrix under a remote external tensile load. The purpose was to understand the effects of neodymium rich particles on the fatigue properties of Ti-55 alloy. Three case studies were considered. First both particle and matrix were perfect, second a crack existed within the particle, and third a crack was located in the matrix adjacent to the particle. Numerical results show that soft particles cause stress concentration in regions of the matrix adjacent to the particle, but that such stress concentrations are much weaker than those associated with a cavity. A crack within the particle increases the stress concentration in the matrix only a little when the crack is far from the interface. However, a crack in the matrix significantly increases local stress in the particle.     

Molecular dynamics simulation and in situ TEM study of crack healing

Abstract

In situ TEM observation of crack healing during heating was carried out in an α-Fe crystal, and the results indicated that a crack in α-Fe could completely heal when the temperature increased to a critical value. The molecular dynamics method was used to simulate crack healing during heating and/or under compressive stress in a Cu crystal. The simulation results showed that a centre crack in a Cu crystal would close under a compressive stress or by heating. The roles of compressive stress and heating in crack healing were additive. During crack healing, dislocations generation and motion occurred. If there were pre-existing dislocations around the crack, the critical temperature or compressive stress necessary for crack healing would decrease, and the higher the number of dislocations, the lower the critical temperature or compressive stress. The critical temperature necessary for a crack to heal depended upon the orientation of the crack plane.     

空心微球/环氧树脂复合泡沫塑料的抗压性能与破坏机制

以环氧树脂为基体, 不同粒径空心玻璃微球为填充体, 制备了轻质高强复合泡沫塑料。通过单轴准静态压缩试验研究了空心微球的粒径大小对复合泡沫塑料的抗压性能的影响, 并采用SEM对复合泡沫塑料的微观结构进行观测。通过随机空间分布法建立了空心玻璃微球/环氧树脂复合泡沫塑料的实体模型, 并且使用有限元分析软件对复合泡沫塑料在1 kPa载荷下的应力分布进行了分析。结果表明, 在相同体积含量下, 当空心微球的粒径从30 μm增大到120 μm时, 复合泡沫塑料的抗压强度无明显变化。有限元分析的结果表明, 在复合泡沫塑料中主要承载部分为空心微球, 空心微球上的应力大于树脂基体上的应力。最大应力分布在空心微球的内壁, 结合SEM图像可推测, 空心微球在破裂之前受到充分的挤压, 并且从内壁产生裂纹。     

Comparison among estimation methods of C* parameter for axially oriented external surface crack in cylinders

Abstract

C^* is usually used to describe the creep crack growth. ASTM E1457 allows C^* to be calculated from creep load line displacement rate. However in components it is difficult or impossible to measure load line displacement rate. Therefore for the components C^* must be determined by finite element methods or reference stress concepts. Estimates of C^* obtained by reference stress methods will depend on the collapse mechanism adopted and therefore several estimations are proposed. This paper presents a numerical study of non-linear fracture mechanics parameter predictions under elevated temperature for axially oriented external surface crack in cylinder. Comparison of C^* calculated from FE analysis and different reference methods is conducted. The values of C^* obtained from the API579 net section solution are also found to be slightly conservative and give the closest agreement to the F.E. contour integral C^*. In addition, the comparison between C^* of homogeneous material and TYPE IV cracking is conducted. The difference between homogeneous material and TYPE IV cracking is almost negligible and therefore the reference stress solutions for homogenous material could be applied to estimate C^* for TYPE IV cracking.     

Numerical prediction of creep crack growth in different geometries using simplified multiaxial void growth model

Abstract

This paper considers the prediction of creep crack growth (CCG) in different fracture mechanics geometries using finite element (FE) analysis based on a material independent simplified multiaxial failure strain model at the crack tip. The comparison is first made by modelling C(T) specimen tests under plane stress and plane strain conditions using creep properties of a C–Mn steel at 360°C. In addition, in order to examine CCG due to different geometries, a single edge notch specimen (SENT), centre cracked tension specimen (CCT) and three-point bending (3PB) specimen have been modelled and analysed. In all cases, it is found, depending on the geometry, that for this steel at low creep temperatures the applied load develops a high reference stress/yield stress (σ_ref/σ_y) ratio, which helps reduce constraint at the crack tip. The predictions are analysed under plane stress/plane strain loading conditions identifying the effects of geometry on cracking rates and the implications for predicting long term test or component failure times exceeding where the applied σ_ref/σ_y<<1.     

Room-temperature creep behavior on crack tip of commercially pure titanium

The room-temperature creep behavior on crack tip of compact tensile (CT) specimen for commercially pure titanium (CP-Ti) was studied by experiment and finite element (FE) simulation in this paper. The experimental results indicated that the time-dependent deformation was observed on the crack tip of CP-Ti CT specimen at room temperature, which agreed with the primary creep, and crack propagation was not observed. In order to consider the creep behavior on crack tip, time-dependent J-integral was used to characterize the stress fields near crack tip. The room-temperature creep behavior on crack tip was analyzed by FE simulation, which was verified by experimental results. Then, the strain fields under different stress states were analyzed by FE simulation. The influences of the locations to crack tip and load on the room-temperature creep were analyzed, which shows that the creep significance on crack tip is enhanced with increasing of load and decreasing of distance to crack tip. The estimation formula of creep strain value along ligament direction of CP-Ti CT specimen was established and verified by FE simulation results.     

Analysis of the effects of compressive stresses on fatigue crack propagation rate

In this study, the effects of compressive stresses on the crack tip parameters and its implication on fatigue crack growth have been studied. Elastic–plastic finite element analysis has been used to analyse the change of crack tip parameters with the increase of the applied compressive stress level.The near crack tip opening displacements and the reverse plastic zone size around the crack tip have been obtained. The finite element analysis shows that when unloading from peak tensile applied stress to zero applied stress, the crack tip is still kept open and the crack tip opening displacement gradually decreases further with the applied compressive stress. It has been found that for a tension–compression stress cycle these crack tip parameters are determined mainly by two loading parameters, the maximum stress intensity K_max in the tension part of the stress cycle and the maximum compressive stress σ_maxcom in the compression part of the stress cycle.Based on the two parameters, K_max, and σ_maxcom, a fatigue crack propagation model for negative R ratios only has been developed to include the compressive stress effect on the fatigue crack propagation rate.Experimental fatigue crack propagation data sets were used for the verification of this model, good agreements have been obtained.     

Surface effects on time-dependent fracture parameter of subsurface crack in plates under tension

Based on the comprehensive finite element (FE) creep analyses, the influence of free surface on the time dependent fracture mechanics parameter of a crack near the free surface in plates under tension has been investigated. It is found that the time dependent fracture parameter C* increases as the crack tip closes to the free surface. Such an increment is related not only to the crack configurations but also to the material properties, especially the creep exponent n of power creep law. In addition, more pronounced interaction is observed between the C* of subsurface crack and that of a single isolated crack compared to that denoted by SIF under the linear elastic fracture condition. Under the framework of reference stress method, we also developed a closed form solution for creep interaction factor. Overall good agreement is achieved between the proposed method for the C* of subsurface crack and the FE results which provides us confidence in practical application.     

Ball Impact and Crack Propagation – Simulations of Particle Compound Material

Particle compounds are the combination of various sized particles with non-uniform properties and can be considered as one of the most complicated engineering materials. The properties of the particle compounds vary in large range depending upon applications, methods of manufacturing and ratios of its compositions. Even if the method of manufacturing is same, the properties may be different because of the arrangements of ingredients. The different types of engineering agglomerates and building materials, like concretes, are some examples of the particle compounds. Similarly, the proper recycling of particle compound is very important in order to utilize the valuable aggregates from the cheaper fine matrixes. The aim of this research is to study the crack initiation and propagation in the building materials of spherically shaped concrete structures under impact loadings. A 2 Dimensional Finite Element Analysis is carried out with central impact loading condition to understand the stress pattern distributions before cracking. The Discrete Element Method (DEM) is adopted for further analysis to study the crack propagation in particle compound. Concrete spheres of diameter 150 mm with properties of B35 (35 N/mm² compressive strength) are chosen for the representation. A sphere is geometrically easier for the analysis. The assumption can be made that after some stages of loading the cube shaped concrete will be similar to sphere after losing its edges. This paper discusses the continuum and discrete approach for the analysis of crack propagation in particle compound with reference to the concrete ball. The analysis is done with central impact loading conditions in different velocities ranges between 7.7 m/s to 39 m/s. The correlations between theoretical simulations and practical experiments are also discussed.KeywordsFracture pattern, Crack propagation, Crack simulation, Air cannon, Numerical simulationThe authors would like to acknowledge German Research Foundation for the financial support.