Size effects in material strength due to crack growth and material non-linearity

Failure by strength and fracture collapse tend to compete with one another when the specimen sizes are varied. Material testing dealing with the determination of tensile strength and hardening is usually carried out with small specimens while the evaluation of fracture mechanics parameters such as critical stress-intensity factor or strain energy density factor requires specimens that are larger in size. The formation of cracks in small specimens does not appreciably affect failure by strength collapse. On the other hand, the fracture process is not disturbed by the development of plastic hinges in the unbroken ligament of the larger specimens.     

Principles of the micromechanics of material damage. 1. Long-term damage

The principles of the theory of long-term damage based on the mechanics of stochastically inhomogeneous media are set out. The process of damage is modeled as randomly dispersed micropores resulting from the destruction of microvolumes. A failure criterion for a single microvolume is associated with its long-term strength dependent on the relationship of the time to brittle failure and the difference between the equivalent stress and the Huber-von Mises failure stress, which is assumed to be a random function of coordinates. The stochastic elasticity equations for porous media are used to determine the effective moduli and the stress-strain state of microdamaged materials. The porosity balance equation is derived in finite-time and differential-time forms for given macrostresses or macrostrains and arbitrary time using the properties of the distribution function and the ergodicity of the random field of short-term strength as well as the dependence of the time to brittle failure on the stress state and the short-term strength. The macrostress-macrostrain relationship and the porosity balance equation describe the coupled processes of deformation and long-term damage __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 2, pp. 108–121, February 2007. For the centenary of the birth of G. N. Savin.     

Computational micromechanics of dynamic compressive loading of a brittle polycrystalline material using a distribution of grain boundary properties

A two-dimensional finite element model is used to investigate compressive loading of a brittle ceramic. Intergranular cracking in the microstructure is captured explicitly by using a distribution of cohesive interfaces. The addition of confining stress increases the maximum strength and if high enough, can allow the effective material response to reach large strains before failure. Increasing the friction at the grain boundaries also increases the maximum strength until saturation of the strength is approached. Above a transitional strain rate, increasing the rate-of-deformation also increases the strength and as the strain rate increases, fragment sizes of the damaged specimen decrease. The effects of flaws within the specimen were investigated using a random distribution at various initial flaw densities. The model is able to capture an effective modulus change and degradation of strength as the initial flaw density increases. Effects of confinement, friction, and spatial distribution of flaws seem to depend on the crack coalescence and dilatation of the specimen, while strain-rate effects are result of inertial resistance to motion.     

On the zero-curvature criterion for structures with material strengthening and geometrical non-linearity

A zero-curvature criterion is proposed to determine the practical collapse load. Six tests have been carried out on spherical pressure vessels with cylindrical nozzle. Results of these tests and other experimental data quoted from different references are discussed in order to compare the new criterion with various previously proposed criteria. It is concluded that: (1) the zero-curvature point is a characteristic point of the experimental curve and that the new criterion is an objective criterion without any artificial coefficient. (2) the deviation of the collapse load estimated by the new criterion is smaller than that estimated by other criteria.Supported by the Chinese National Foundation of Natural Science.     

Computational micromechanics model for the convection of a cracks population in a brittle material

We stated in Sánchez et al. (Proc. 15th IMACS World Congress, Vol. 5, 1997, p. 513), the objective rate law governing the general evolution, nucleation, growth and convection, of a diluted 3D population of arbitrarily oriented, penny-shaped, non-interacting stable microcracks that is dragged along the flow of a regular motion of a simple continuous body of brittle material.This requires the prior analysis of the convection process in the hypothesis of ignoring crack nucleation. It follows that the evolution of the microcrack population is here due only to the rotation of the crack planes as a consequence of the deformation processes of the microcracked brittle solid.The determinant role of this case in the general evolution problem, is also so in its numerical treatment.In this paper, use is made of the Bubnov–Galerkin spectral method with respect to the angular variable defining the orientation of a crack to numerically solve the mathematical model of the pure convection of microcracks in the no-nucleation hypothesis.The paper is completed with three applications. The corresponding microcracks evolutions have been graphically displayed showing a behaviour that agrees with the expected.Indications about the computer codes implementing the numerical algorithm are included in an appendix.     

Modeling the deformability of a material

The high-temperature extension of metals to fracture is modeled for creep at constant stress or at constant strain rate. The dependence of the ultimate fracture strain on the loading factor (stress or strain rate) is studied. The nonmonotonic nature of this dependence with an internal maximum is described using the Rabotnov kinetic theory with one and two damage parameters. Available experimental data are analyzed. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 5, pp. 183–188, September–October, 2007.     

On the motion of a material point on a moving surface

Summary Sufficient conditions are given for the stability and instability of the equilibrium position x=y=z=0 in the mechanical system consisting of a material point constrained to move on the moving surface z=−λ(t)(x²+y²) (λ(t)>0) in a constant field of gravity (the axis 0z is directed vertically upward) under the action of viscous friction of total dissipation.

---

Sommario Si danno condizioni sufficienti per la stabilità e la instabilità della posizione di equilibrio x=y=z=0 nel sistema meccanico che consiste di un punto materiale vincolato a muoversi sulla superficie mobile z=−λ(t)(x²+y²) (λ(t)>0) in un campo di gravità costante (l'asse 0z è diretto verticalmente e orientato verso l'alto) sotto l'azione di attriti viscosi con dissipazione completa.

     

Primary resonance of multiple degree-of-freedom dynamic systems with strong non-linearity using the homotopy analysis method

A homotopy analysis method（HAM）is presented for the primary resonance of multiple degree-of-freedom systems with strong non-linearity excited by harmonic forces.The validity of the HAM is independent of the existence of small parameters in the considered equation.The HAM provides a simple way to adjust and control the convergence region of the series solution by means of an auxiliary parameter.Two examples are presented to show that the HAM solutions agree well with the results of the modified Linstedt-Poincar＇e method and the incremental harmonic balance method.     

Modeling of the metal powder compaction process using the cap model. Part I. Experimental material characterization and validation

In order to produce crack free metal powder compacts that respect both the dimensional tolerances and the mechanical strength requirements, both tooling design and compaction sequence have to be adequately determined. The finite element method, through the use of an appropriate constitutive model of the powder medium, has recently been used as an efficient design tool. The accuracy of this method highly depends on the faithfulness of the constitutive model and the quality of the material parameter set. Furthermore, in order for the simulation results to be reliable, they should be experimentally validated on real parts featuring density variations. Hence, the main concerns of this paper are the development of a standard calibration procedure for the cap material model as well as the development of a reliable technique for the experimental validation of the powder compaction simulation results.The developed calibration procedure, applied for the case of 316L stainless steel powders, is based on a series of isostatic, triaxial and uniaxial compaction tests as well as resonant frequency tests. In addition, a sensitivity study was performed in order to determine the relative importance of each factor and basic simulations served to validate the parameter set extraction procedure.On the other hand, a local density measurement technique was developed for the experimental validation of the model results. This technique is based on correlation with Vickers macro-hardness. Finally, an application featuring the compaction of a 316L stainless steel cylindrical component is presented to illustrate the predictive capabilities of the cap material model as well as the accuracy of the acquired material parameter set.     

Modeling the effect of moisture on the flowability of a granular material

Meccanica - The flowability of granular materials is a crucial parameter to consider that impacts many engineering and industrial applications such as slope stability, powder handling and storage....     

Modeling the process of melt solidification on the surface of a material

Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 2, pp. 122–126, March–April, 1992.     

Nonlinear oscillations of sigmoid functionally graded material plates moving in longitudinal direction

Geometrically nonlinear oscillations are investigated on sigmoid functionally graded material(S-FGM) plates with a longitudinal speed. The material properties of the plates obey a sigmoid distribution rule along the thickness direction. Based on the D'Alembert's principle, a nonlinear equation of motion is derived for the moving S-FGM plates, where the von Kármán nonlinear plate theory is adopted. Utilizing the Galerkin method, the equation of motion is discretized and solved via the method of harmonic balance. The approximate analytical solutions are validated through the adaptive step-size fourth-order Runge-Kutta method. Besides, the stability of the steady-state solutions is examined. The results reveal that the mode interaction behavior can happen between the first two modes of the moving S-FGM plates, leading to a complex nonlinear frequency response. It is further found that the power-law index, the longitudinal speed, the excitation amplitude, and the in-plane pretension force can significantly affect the nonlinear frequency-response characteristics of longitudinally traveling S-FGM plates.     

Pre-kinking of a moving crack in a magnetoelectroelastic material under in-plane loading

A constant moving crack in a magnetoelectroelastic material under in-plane mechanical, electric and magnetic loading is studied for impermeable crack surface boundary conditions. Fourier transform is employed to reduce the mixed boundary value problem of the crack to dual integral equations, which are solved exactly. Steady-state asymptotic fields near the crack tip are obtained in closed form and the corresponding field intensity factors are expressed explicitly. The crack speed influences the singular field distribution around the crack tip and the effects of electric and magnetic loading on the crack tip fields are discussed. The crack kinking phenomena is investigated using the maximum hoop stress intensity factor criterion. The magnitude of the maximum hoop stress intensity factor tends to increase as the crack speed increases.     

On the micromechanics of void growth by prismatic-dislocation loop emission

Experimental evidence and recent molecular dynamics simulations of void growth indicate that prismatic dislocation loop emission by externally applied stresses is a viable mechanism of void growth under shock loading conditions when diffusive processes are given no time to operate. In this paper, the process of growth by loop emission is studied in a model system comprised of a void in an infinite linearly elastic and isotropic solid loaded axisymmetrically by remote applied stresses. First, the interaction between applied stresses, the stress field of a single dislocation loop or a pile-up of loops next to the void, the surface energy expenditure on void surface change, and the lattice resistance to the motion of loops is reviewed. The necessary condition for interstitial loop emission is used to determine the equilibrium positions of the loops as well as the maximum number of loops in a pile-up under given applied stresses. For the parameters of the model-material with purely hydrostatic loading, the numerical results yield a volume change for the void, which when normalized by the initial undeformed volume, exhibits a strong dependence on the size of the void for radii less than ∼400 times the lattice Burgers vector. For larger voids, the normalized volume change was found to be independent of the void radius.     

On the interaction of non-linearity and dispersion in wave propagation

Summary It is possible to approach non-linear optics from the point of view of field theory. The central problem then is the interaction of non-linearity and dispersion. A simple example of this phenomenon is furnished by Boussinesq's equation in hydraulics.In this paper the derivation and the range of validity of this equation are discussed. It is shown that the equation can be reduced to one of a simpler type. Some properties of this reduced equation are given.     

Numerical analysis of breaking waves using the moving particle semi-implicit method

The numerical method used in this study is the moving particle semi-implicit (MPS) method, which is based on particles and their interactions. The particle number density is implicitly required to be constant to satisfy incompressibility. A semi-implicit algorithm is used for two-dimensional incompressible non-viscous flow analysis. The particles whose particle number densities are below a set point are considered as on the free surface. Grids are not necessary in any calculation steps. It is estimated that most of computation time is used in generation of the list of neighboring particles in a large problem. An algorithm to enhance the computation speed is proposed. The MPS method is applied to numerical simulation of breaking waves on slopes. Two types of breaking waves, plunging and spilling breakers, are observed in the calculation results. The breaker types are classified by using the minimum angular momentum at the wave front. The surf similarity parameter which separates the types agrees well with references. Breaking waves are also calculated with a passively moving float which is modelled by particles. Artificial friction due to the disturbed motion of particles causes errors in the flow velocity distribution which is shown in comparison with the theoretical solution of a cnoidal wave. © 1998 John Wiley & Sons, Ltd.     

Subharmonic solutions of the duffing equation with large non-linearity1

The subharmonic solutions of order $\text{1}\text{3}$ of the damped Duffing equation are determined in a suitable parametric form, following the procedure recently developed in [8, 9], and are compared with the results obtained by direct numerical integration of the same equation, carried out with respect to the time with the Runge-Kutta method. It can be deduced that the analytical solution gives satisfactory results in the approximation of the ‘predominantly’ subharmonic solutions of the above equation, even if the non-linearity of the system is very large.     

A computational micromechanics constitutive model for the unloading behavior of paper

In this study, a computational micromechanics material model for the unloading behavior of paper and other nonwoven materials is presented. The asymptotic fiber and bond (AFB) model for paper elastic–plastic behavior [Sinha, S.K., Perkins, R.W., 1995. Micromechanics constitutive model for use in finite element analysis, In: Proceedings of the 1995, Joint ASME Applied Mechanics and Materials Summer Meeting, Los Angeles, CA, USA, Jun 28–30, 1995] has been extended to model the unloading process through a computational algorithm and implemented using the UMAT subroutine in ABAQUS finite element code. For every unloading increment, the material model assumes elastic unloading with a slope equal to the initial elastic modulus. The Jacobian matrix of the constitutive model is updated at every unloading increment by applying the incremental form of AFB model for a planar element with an elastic fiber and bond condition. A uniaxial tensile and a biaxial Mullen burst loading–unloading experiments were carried out for a paperboard sample and simulated using the model. The stress–strain curve and residual strain for the uniaxial loading were in good agreement with experimental results. The finite element model of the burst test with the AFB unloading material model predicted the general shape of the pressure versus deflection curve. However, the model over predicted the residual deflection by more than 50%. The loading portion of the pressure–deflection curve had a significant offset from experimental curves, and the nonlinearity in the unloading curve towards the end was not predicted. The discrepancies with experimental results are attributed to the burst test itself, model parameter estimation inadequacies, boundary conditions used in the FEA, and neglecting time-dependant effects. Nevertheless, the model can be useful in parametric studies relating microstructure to unloading behavior in structural problems.