Effect Of Material Inhomogeneity Research Articles

The asymptotic solution of the elasticity theory problem for a radially inhomogeneous cylinder

The elasticity theory problem for a radially inhomogeneous cylinder of small thickness, whose elastic moduli are arbitrary continuous functions depending on the radius of the cylinder, is considered. It is assumed that the side surface of the cylinder is stress-free, and the boundary conditions that keep the cylinder in equilibrium are given at its seats. Asymptotic solutions are constructed by the asymptotic integration method. It is shown that the asymptotic solution consists of the sum of the penetrating solution, simple boundary effect and boundary layer solutions. The character of the stress-strain state corresponding to the penetrating solution, simple boundary effect and boundary layer solutions is determined. Asymptotic formulas are obtained for displacements and stresses, which allow to calculate the stress-strain state of a cylinder.The problem of torsion of a radially inhomogeneous cylinder is studied, with its lateral surface free from stress and the boundary conditions keeping it in equilibrium at its seats. By applying the asymptotic integration method, it is determined that the asymptotic solution for the torsion problem consists of the sum of the penetrating solution and boundary layer solutions.Numerical analysis is performed and the effect of material inhomogeneity on the stress-strain state of the cylinder is evaluated.

A new insight to investigate the strain distribution, evolution, and crack development of cement-stabilized coral aggregate

Cement-stabilized coral aggregate (CSCA) can be used as a base material for roads and airports in island engineering. In this study, four-point bending (FPB) tests were conducted on CSCA with different prefabricated crack depths, and distributed fiber optic sensor (DFOS) was used. The testing process of the CSCA beams was simulated using an improved bond-based peridynamic (BBPD) model that combines the bilinear damage principle and fracture parameters random field. The results indicate that DFOS has the potential to monitor strain evolution and detect crack in CSCA. The strain distribution in the spanwise direction of the beam during the plastic phase presents a single peak, which can be described by a Pearson-VII function. The fracture location can be predicted from the positions of the tensile strain peaks. The neutral axis begins to move gradually toward the compressed part of the specimen after the external load greater than 0.6 Pmax. The compression modulus of the CSCA material peaks is 4500 MPa, that is three times larger than its tensile modulus and can satisfy the requirement of semi-rigid base layer construction of island roads. The improved BBPD model is able to effectively simulate the strain-softening behavior of CSCA materials with consideration of the effect of material inhomogeneity on the actual fracture path. The peak load prediction error was less than 7 %. The R2 between the numerically predicted load-displacement curves and the test results were bigger than 0.95. The improved BBPD method can predict the actual fracture location of the specimen with a horizontal position deviation of less than 2 cm. The bending fracture process of CSCA are further explored from both experimental and numerical simulations by this study.

A multiscale fracture model to reveal the toughening mechanism in bioinspired Bouligand structures

The Bouligand structure has been observed in a variety of biological materials, such as lamellar bone and exoskeleton of lobsters. It is a hierarchical and non-homogeneous architecture that exhibits excellent damage-resistant performance. This paper presents a multiscale fracture model considering the material inhomogeneity, the multiscale property, and the anisotropy to reveal the toughening mechanisms in the Bouligand structure. Firstly, the macro and micro constitutive properties of this composite are derived. Then, a multiscale fracture model is developed to characterize the local stress intensity factors and the energy release rates at the crack front of twisted cracks. Our results demonstrate that the decrease in the local energy release rate can be attributed to two-step mechanisms. The first mechanism is that the multiscale structure and the material inhomogeneity cause a release of stress near the initial crack tip. The second mechanism is that the twisted crack leads to the transformation from single-mode loading to mixed-mode loading, which enhances the fracture toughness. These results can not only reveal the toughening mechanism of the Bouligand structure but also provide guidelines for the design of high-performance composites. Statement of significanceBiological materials in nature often possess excellent mechanical properties that have not been achieved by synthetic materials. Bioinspired Bouligand structures provide prototypes for designing high-performance materials. In this study, we propose a multiscale theoretical fracture model to investigate the fracture properties of Bouligand structures with twisted cracks. We systematically consider the roles of material inhomogeneity, anisotropy, and multiscale properties. Our analysis demonstrates that the remarkable toughness of Bouligand structures results from the combined effects of material inhomogeneity and twisted cracks. This research contributes to unveiling the secret behind the outstanding toughness of Bouligand structures and provides inspiration for the development of novel designs for man-made composites.

Effect of material inhomogeneity on constraint loss measured with subsized C(T) fracture specimens of a reactor pressure vessel steel

In this study, the fracture behavior of the low-alloy reactor pressure vessel JRQ steel was investigated in the ductile-to-brittle transition region with two different subsized compact tension fracture specimens: 0.18T C(T) and 0.5T C(T). The specimens were extracted from two thin plates (surface and middle) of the large JRQ steel plate, which is well-known to be macroscopically inhomogeneous in terms of brittleness. In particular, the reference temperature T0 as defined in the ASTM-E1921 standard was calculated for the two plates with the 0.18T C(T) and 0.5T C(T) specimens. A significant difference in the reference temperature T0 of more than 90 °C as determined with the 0.5T C(T) data was found between the two plates indicating a clear macroscopic inhomogeneity between the two depths. The measured toughness of 0.18T C(T) specimens and corresponding T0 evaluation showed that the effect of constraint loss was more pronounced for the middle plate due to its lower strength and that the constraint loss effect can be confounded with inhomogeneity. A local approach to fracture model was applied to account for the constraint loss by calibrating a criterion based on critical stressed volume V* and critical stress σ* obtained by finite element simulations. A big difference in the local fracture stress σ* between the two plates was found and based on the deduced local criterion it was shown that the measured 0.18T toughness can be effectively predicted within the temperature range of the ductile-to-brittle transition.

Synthetical effect of material inhomogeneity and welding defects on fatigue behavior of 2205 duplex stainless steel cruciform welded Joints: Experiments and Life-prediction model

This paper performed experimental and analytical investigations on the synthetical effect of material inhomogeneity and welding defects on the fatigue behavior of 2205 duplex stainless steel cruciform welded joints. A series of experiments were performed, including microstructure characterization by the electron back-scattered diffraction, fatigue mechanical tests assisted by digital image correlation technique and fracture morphology observations by scanning electron microscope. Results show that fatigue life and failure location of cruciform welded joints depended heavily on their geometric configurations for lower cyclic amplitudes. However, with the elevation of loading, material inhomogeneity played a greater roles, leading to the change of fatigue failure mode with both geometric configuration and cyclic stress amplitude. To quantize the effects of welding defects and material inhomogeneity, a modified structure strain method was proposed by considering the heterogeneous plastic properties, to accurately predict both fatigue lifetime and failure location of cruciform welded joints at both low and high cycles fatigue. Lastly, a damage tolerance-based fatigue design method was discussed to guide the highly-reliable manufacture and damage detection of duplex stainless steel cruciform welded joints in the engineering.

Impact behaviour of dry granular flow against baffle structure: coupled effect of Froude and particle characteristics

The baffle design resisting dry granular flow is still impeded by the effect of the particle size distribution coupled with the influence of Froude characteristics on baffle performance – for example, the deceleration process and run-up process. Based on discrete-element method simulation, this study investigated the baffle deceleration and granular flow run-up. Baffle deceleration is controlled by the change of particle contact behaviour behind the baffle slits and is more sensitive to the particle size than the Froude characteristics of granular flow. Although the granular flow run-up height is also affected by the debris–slit interaction, it is mainly dominated by the flow climbing along the baffle, which is more sensitive to the Froude characteristics and stress-transfer mechanism. Bidisperse granular flow has more complex interaction with the baffle compared with monodisperse flow. The effect of material inhomogeneity on baffle performance depends on the particle content. For baffle design, the first array can be considered as a reference. The estimation of the baffle deceleration potential and height with consideration to unsteady dynamics and material inhomogeneity is also presented in this paper.

Effect of Material Inhomogeneity on the Crack Tip Mechanical Field and SCC Growth Rate of 52M/316L Dissimilar Metal Welded Joints

The stress–strain conditions at the crack tip in dissimilar metal welded joints (DMWJ) are a critical factor influencing stress corrosion cracking (SCC) behavior. The processing technology and working environment of DMWJ lead to a randomly inhomogeneous distribution of material mechanical properties, making the crack tip mechanical field more complex. An inhomogeneous model was obtained using a combination of physical experiments and the elastic–plastic finite element method to understand the effect of this inhomogeneous distribution of mechanical properties on the direction of SCC growth and the growth rate in DMWJ and the impact of inhomogeneity on the SCC growth behavior was compared and analyzed. The findings demonstrate that Type I (opening mode) cracks are more likely to form due to the inhomogeneity of mechanical properties and are more likely to deflect toward the Alloy 52M region at the interface between Alloy 52M and 316L stainless steel. Additionally, the strain gradient at the crack tip increases with the degree of inhomogeneity, which has a bigger impact on the accuracy of SCC growth rate predictions.

Plasto-elastohydrodynamic lubrication of heterogeneous materials in impact motion

The analysis of plastic evolution and material inhomogeneity is required for an accurate description of lubrication under impact loading. This work develops a semi-analytical model for heterogeneous materials in impact motion under plasto-elastohydrodynamic lubrication (PEHL) with limited inlet oil. A plasticity loop is proposed to obtain the accumulative plastic strain iteratively based on the analysis of the stress state. The inhomogeneous inclusion within the materials is homogenized with unknown eigenstrains according to the equivalent inclusion method. The surface displacements induced by the plastic strains and eigenstrains are introduced into the gap between the contact bodies to update the lubrication film thickness until the convergence is achieved. The consideration of plastic strains and eigenstrains makes the model more realistic for PEHL under impact loading. The responses including the pressure, film thickness, starvation parameter, residual deformation, temperature, and subsurface elastoplastic fields during the impact–rebound process are discussed. After the model validation against the reference data, the effects of material inhomogeneity and strain hardening on the lubrication response, as well as the typical features of elastic perfectly-plastic materials, are investigated to provide guidance for material reliability analysis.

Influence of layer architecture on fracture toughness and specimen stiffness in polymer multilayer composites

The objective of this contribution was to increase the fracture toughness of talcum reinforced polypropylene (PP) while preserving specimen stiffness. This was accomplished by introducing soft interlayers (ILs) made of standard PP (PP-St) or very compliant PP (PP-Soft) and utilizing the so-called material inhomogeneity effect. Architectures with one or two ILs of either 0.3 or 0.9 mm thickness were tested in single edge notched bending experiments. Layers of PP-Soft always arrested growing cracks due to their low Young’s modulus, E, and yield stress, σy, which is called an (E-σy)-inhomogeneity. However, the increase in fracture toughness came at the cost of specimen stiffness. For ILs made of PP-St, E was still lower compared to the matrix material, but σy was similar (pure E-inhomogeneity). Specimen stiffness remained high for these composites, but crack arrest could not be achieved in most cases, which could be explained by plastic deformation of the soft layers. Plastic deformation could be contained within the ILs in one of the architectures, where two large ILs were used. Crack arrest could be achieved in this adapted IL design, leading to excellent fracture toughness in combination with high stiffness.

A novel approach for determining the stress intensity factor for cracks in multilayered cantilevers

In modern engineering applications, multilayered structures are extensively used. The material property variations between the layers affect the fracture behavior of the multilayer by the reduction or enhancement of the crack driving force. This “material inhomogeneity effect” complicates the determination of the stress intensity factor of cracks in multilayered components, and a combination of experimental measurements and numerical computations was necessary to determine correctly the fracture toughness. A procedure is presented in this paper, which enables the simple determination of the stress intensity factor from analytic relations, without numerical analysis. These relations are valid for multilayered cantilevers and multilayered three-point bend specimens with variations of the Young’s modulus. The procedure can be also used for the design of tough multilayered composites. The procedure is verified for different multilayer configurations by finite element computations and validated with the help of experimental results from literature.

Influence of the material inhomogeneity effect on the crack growth behavior in fiber and particle reinforced composites

If a crack grows through a material with variations in Young’s modulus, a variation in the crack driving force occurs at a constant loading. Recent papers have shown that this material inhomogeneity effect has a great influence on the crack growth behavior and the fracture toughness of the materials. The purpose of this paper is to investigate the material inhomogeneity effect in fiber- or particle reinforced materials where the crack circumvents the particles and grows only through the homogeneous matrix material. A finite element study is performed under application of the configurational force concept. The particles cause a spatial variation of the crack driving force, quantified by the near-tip J-integral, Jtip. Characteristic parameters of the Jtip-variation are determined as a function of the composite geometry and the matrix and particle properties. The study is made for a regular arrangement of particles, but the results can be also applied for composites with arbitrary particle locations. Implications for the fracture toughness of the composite are worked out. The validity limits of the numerical results and the deduced analytical expressions are discussed.

Effect of material inhomogeneity on chatter stability

Chatter vibrations in milling are a widely researched topic in manufacturing science. The models used to predict and mitigate chatter use assumptions for the model inputs. Assuming the workpiece material is homogenous, is such an assumption. In this study, the effect of workpiece material variation on chatter stability is studied. Upon the observation of varying stability limits during milling operations of aluminium blocks, it is shown that the workpiece material inhomogeneity affects the chatter stability. To support this hypothesis, the surface hardness of the workpieces is measured using the Leeb rebound hardness test method. It is shown that the location-dependent chatter stability limits, calculated using the local cutting coefficients, capture the position-dependent stability nature of the experimental data.

Effect of material inhomogeneity under creep and plastic to creep transition of cracks

The driving force of a crack in a non-linear elastic material is described by the conventional J-integral, J (Rice 1968). For elastic−plastic materials, J does not describe the crack driving force. However, it describes the intensity of the crack tip field and can be, therefore, used to quantify the fracture toughness (Rice 1968). For the high-temperature behaviour of materials where creep deformation dominated, analogous parameter to J-integral were deduced, the C*-integral and a similar parameter, the Ct-integral (Landes and Begley 1976). C* has been proven to have a good correlation with the creep crack growth rate for many materials, mostly under extensive creep conditions. However, it does not describe the crack driving force.Based on the concept of configurational forces, a J -integral for elastic–plastic materials, Jep, was derived, which is able to quantify the true crack driving force in accordance with incremental theory of plasticity [4]. Hereby, the plastic strain is treated as an eigen-strain. Jep can be applied also in cases of non-proportional loading, e.g. for a growing crack (Simha et al. 2008) or for cyclic loading conditions (Ochensberger and Kolednik 2015). In this work, the concept of configurational force is applied to evaluate the crack driving force under small, medium and extensive creep conditions. Hereby, the creep strain is treated as a time dependent eigenstrain. A case study is performed where the path dependences of the elastic–plastic J-integral, Jep, and the conventional parameters Ct and C* are studied for materials which undergo elastic+creep deformation, with material inhomogeneity.It has been confirmed in the recent studies (Kolednik et al. 2014, Tiwari et al. 2020) that the material inhomogeneity term affects the crack depending on the nature of material inhomogeneity. This effect is unknown for creep deformation and the same has been studies on idealized fracture specimen under creep deformation using configurational forces and finite element method simulating real situations of dissimilar metals used at high temperatures in nuclear power plants and jet engines.

Effect of Material Properties in the Direct and Inverse Thermomechanical Analyses of Multilayer Functionally Graded Solids

Herein, the effect of material inhomogeneity on the temperature and stress distributions in functionally graded solids is analyzed. Assuming the inaccessibility of the inner surface of a multilayer functionally graded hollow sphere for the direct monitoring of the temperature in real time, the problem on identifying the temperature on this surface is formulated by implementing the temperature and circumferential strain given on the outer surface. The material properties within each sphere layer are assumed to be arbitrary functions of the radial coordinate. By representing the material properties of the sphere in the form of stepwise‐variable functions and implementing the generalized derivative technique, a method for the reduction of the formulated problem to an inverse thermoelasticity problem is developed. Using the finite difference method, a numerical algorithm for solving the inverse problem is suggested. The stability of the proposed numerical algorithm concerning the input perturbation is verified.

Delamination analysis of multilayered beams exhibiting creep under torsion

A delamination analysis of a multilayered inhomogeneous beam structure under linear creep is developed. A viscoelastic model that consists of an arbitrary number of linear springs and linear dashpots is used. The cross-section of the beam is a circle. The beam is made of concentric longitudinal layers. Each layer is continuously inhomogeneous in thickness and length directions. Therefore, the shear moduli and the coefficients of viscosity of the viscoelastic model are distributed continuously along the thickness and length of each layer. Two concentric delamination cracks are located arbitrary between layers. The beam is loaded in torsion. Time-dependent solutions to the strain energy release rate for the two delaminations are derived by using the time-dependent strain energy in the beam. The strain energy release rates are derived also by the compliance method for verification. The variation of the strain energy release rate with time due to creep is evaluated. The effects of material inhomogeneity, external loading and delamination length on the strain energy release rate are investigated.

Modeling and FEM simulation of a pressurized and rotated functionally graded thick walled cylinder

ABSTRACT The present study investigates the effect of material inhomogeneity on thick cylinders under rotation with uniformly applied internal and external pressure. In line with that, a finite element method (FEM)-based simulation is performed for the elastic analysis of thick cylinders made of functionally graded materials (FGMs). The property of FGMs is assumed in an exponential functional form of radial position with a constant Poisson’s ratio. Stress distributions along the radial and circumferential directions are studied, considering the stress in an axial direction to be zero. The results show that the property of FGMs has a significant influence on stress distributions by reducing the overall radial stress and completely changing the distribution of circumferential stress compared to an isotropic cylinder under the same load. Thus, the use of exclusively designed FGMs for manufacturing parts can increase their pressure handling capacity and improve their functionality.

Analysis of internal delamination in multilayered rod in torsion

A multilayered inhomogeneous rod with an internal delamination crack loaded in torsion is analyzed. The crack has a circular cross-section. The delamiantion is located symmetrically with respect to the middle of the rod. The layers exhibit continuous material inhomogeneity in radial and length directions. The material properties are distributed symmetrically with respect to the middle of the rod. In order to obtain the torsion moments in the crack arms, the rod is treated as a structure with one degree of internal static indeterminacy. The delamination is studied in terms of the strain energy release rate by using the compliance method. Effects of material inhomogeneity, length and location of the crack on the delamination behaviour are investigated.

Оценка анизотропии механических свойств листового проката из углеродистой стали

The purpose of the article is to establish experimentally the effect of material inhomogeneity on the characteristics of strength ( σ в, σ 0.2) and plasticity (δ) on example of a rolled steel sheet. Uniaxial tensile testing was carried out on flat samples of hot-rolled sheet made of St3 alloy cut in three directions relative to rolling: along, across and at the angle of 450. The heterogeneity of structure was established by studying the fracture surface of the destroyed samples after tensile testing. A metallographic research and micromechanical testing (measurement of microhardness) of sections parallel to the fracture surface were carried out as well. The uniaxial tensile testing of flat samples resulted in obtaining the values of the characteristics of strength ( σ в, σ 0.2) and plasticity (δ). The analysis of fracture patterns, microstructure and microhardness values of the material allowed to reveal the structural heterogeneity caused by the presence of fibrousness and a banded ferrite-pearlite structure oriented along the deformation direction. The formation reason of the latter was the presence of oriented non-metallic inclusions - elongated plastic sulfides. The study determined that the material under investigation features the anisotropy of mechanical properties and structural heterogeneity. The values of the ultimate strength ( σ в) and yield strength ( σ 0.2) decrease from the longitudinal direction to the transverse direction (relative to the rolling direction) and vice versa (from the transverse to longitudinal direction) in the first case probably due to the influence of non-metallic inclusions (plastic sulfides) and, as a result, the banded ferrite-pearlite structure; in the second case due to the influence of fiber direction. The values of the relative elongation (δ) decrease from the longitudinal direction to the direction at an angle of 450 and then increase to the transverse direction as a result of different hardening of the material during plastic deformation. This is proved by the obtained microhardness values of the investigated sections and the values of the maximum applied loads during the tensile test. The obtained values are obviously the result of the influence of fiber orientation relative to the existing maximum tensile stresses.

Surface instabilities in graded tubular tissues induced by volumetric growth

Growth-induced pattern formation in tubular tissues is intimately correlated to normal physiological functions. Moreover, either the microstructure or certain diseases can give rise to material inhomogeneity, which can lead to a change of shape in the tissue. Therefore, it is of fundamental importance to understand surface instabilities and pattern transitions of graded tubular tissues. In this paper we perform such analysis by the use of a mechanical model of a graded tube which grows with a fixed outer boundary by focusing on a plane-strain problem within the framework of nonlinear elasticity. A theoretical model is established to determine the uniform growth state, the critical growth factor, and the critical wavenumber for a general material model and for a general material gradient. For a case study, the material is specified by the neo-Hookean model, and the shear modulus is assumed to decay linearly or exponentially from the inner surface. Then, a parametric study is carried out to unravel the effects of material and geometrical parameters on the bifurcation threshold and the associated wrinkled pattern. In addition, a finite element model, which is validated by the theoretical one, is developed to trace the post-buckling evolution. It is found that wrinkled pattern will evolve into an arch mode and then into a creasing mode if the modulus decays linearly. However, the typical creasing mode may give way to a period-doubling mode when applying an exponentially decaying modulus, and there is a co-existence of the creasing mode and the wrinkling mode. As a result, different modulus gradients can generate diverse pattern formations. The obtained results are useful to supply insight into the effects of material inhomogeneity and different modulus gradients on surface instabilities and morphology evolutions in graded tubular tissues.

Effect of material anisotropy on rolling contact fatigue life under dry and lubricated point contact conditions: A numerical study

Rolling bearings have to operate reliably and efficiently under increasingly severe conditions. Previously ignored effects of material inhomogeneity with varying crystallographic orientation may significantly affect rolling contact fatigue life. In this paper, it is demonstrated that Multigrid techniques allow the computational analysis of such effects in a full 3D setting. Using grain configurations created by Voronoi tessellation, the dependence of the maximum von Mises stress, and of a predicted fatigue life stress field integral with load, friction, mean grain size and crystallographic orientation distribution is shown. Crystallographic orientation variations are shown to potentially significantly reduce predicted rolling contact fatigue life relative to homogeneous isotropic material. The results contribute to material optimization and to computational diagnostics of criticality of material crystallographic (sub)structures.