Mechanics of Materials最新文献

Nowadays, finite element (FE) codes are increasingly employed for simulating large deformation problems. Thus, to reliably represent the strain hardening behavior, a proper calibration of constitutive laws is essential. Focusing on tensile tests, the main issue with ductile metals is necking occurrence, because of the consequent triaxiality and non-uniformity of the strain and stress states. Over the past decades many strain hardening identification approaches have been proposed. Among them, FE-based inverse methods are widely used, but computationally expensive and time consuming. Hence, the authors propose an efficient method which exploits a database for relating the plastic flow rule and the specimen necking profile. The explicit solver of the nonlinear FE code LS-DYNA was used to build the database, whose size could be limited thanks to physical considerations. The developed methodology was applied to experimental quasi-static tensile tests performed on different metals. The predicted hardening laws showed good agreement with those identified with FE-based inverse methods, thus verifying the applicability of the proposed strategy. This study paves the way for machine learning tools having as main input the necking shape: indeed, the present work suggests their feasibility and provides insights into how to establish datasets for a proper and efficient training.

When used in bulk applications, mechanical metamaterials set forth a multiscale problem with many orders of magnitude in scale separation between the micro and macro scales. However, mechanical metamaterials fall outside conventional homogenization theory on account of the flexural, or bending, response of their members, including torsion. We show that homogenization theory, based on calculus of variations and notions of Gamma-convergence, can be extended to account for bending. The resulting homogenized metamaterials exhibit intrinsic generalized elasticity in the continuum limit. We illustrate these properties in specific examples including two-dimensional honeycomb and three-dimensional octet-truss metamaterials.

Additively manufactured lattice structures are porous light-weight structures with mechanical properties that are dictated both from the topology and the parent material properties. When printed from metals, these structures can withstand large continuous plastic deformation. In this paper, we focus on body-centered cubic (BCC) lattice structures under compression up to large deformation strains, and we propose relations between the slenderness ratio of struts and the following mechanical properties: Young's modulus, yield strength, hardening rate of the structure and the densification strain. We perform a systematic study using finite element modelling (FEM) to find how both material properties and lattice structures are affecting the effective mechanical properties of BCC lattice structures under compression. Based on this analysis we propose the scaling laws of the mechanical properties. The scaling laws can be explained as an extension of the Gibson-Ashby power law relations for bend-dominated structures with non-slender beams. We also discuss how rounding the connections between the struts using fillets affects the scaling laws. We demonstrate the scaling laws in the analysis of experimental results, showing the accuracy and limitations of the scaling laws in predicting the mechanical properties, with an emphasis on large deformations. In the analysis, we use experimental values published in literature, and we also present here experimental results of lattice structures printed from Inconel 718.

Additive manufacturing (AM) techniques have been used in several fields of science and industry, and fabrication techniques are being updated. For this fact, especially, for industrial use, mechanical property evaluation methodologies for AM products and standards for product quality assessment should also be well established. In this paper, a probabilistic evaluation of the homogenized elastic properties of a resin product fabricated by a material extrusion-based AM technique is attempted by considering the randomness of both material and microscopic geometrical quantities. This AM method fabricates a resin structure by piling up melted resin, and to decrease consumed material and influence of thermal deformation, the inner structure of the fabricated products will include many pores and its geometry is difficult to be well controlled. From this fact, the products will be regarded as a heterogeneous material with complex random microstructure. This will cause difficulty in the evaluation of its apparent material properties and therefore a probabilistic homogenization analysis is attempted for their quantitative estimation in this study. In particular, to investigate probabilistic properties of microscopic geometry, a random field modeling technique is employed for the evaluation of autocorrelation of the microscopic geometrical parameter, and the results of the autocorrelation identified by experimental observation are introduced to the probabilistic homogenization analysis. The two-dimensional or three-dimensional random field modeling is attempted, and the effectiveness of this approach is investigated by comparing it with the experimental result.

In the current work, the initial yield behavior of closed-cell aluminum foams with three different relative densities under complex stress states have been investigated. A total of 16*3 (three different relative densities of closed-cell aluminum foam) experiments were conducted, which included uniaxial compression, uniaxial tension, combined tension-shear, and triaxial compression tests. Experimental results show that the initial yield behavior of closed-cell aluminum foam is isotropic and is associated with the first invariant of stress tensor, the second and third invariants of deviatoric stress tensor. A constitutive model to describe yield behavior of closed-cell aluminum foam was proposed and the relationship between the first invariant of stress tensor and the second invariant of deviatoric stress tensor was analyzed. Furthermore, tension-compression strength asymmetry of foams was introduced in the proposed model.

The plastic behavior of microscale lath martensite samples is highly anisotropic. Depending on the orientation, the deformation of such samples may be heterogeneous, with only a few localized slip traces, while the remainder of the sample remains largely elastic. Although several continuum plasticity models that account for the anisotropy exist, they cannot reproduce the heterogeneous response observed in experiments. In this study, a model for lath martensite at the microscale is proposed which captures the orientation-dependent heterogeneous behavior observed in experiments. Before formulating the model we first study in detail two idealized cases, in which two different deformation mechanisms are activated. In both cases, the lath martensite is modeled using a discrete slip plane model. In the model, the activation stress of the individual slip systems varies randomly in space according to a distribution based on the underlying dislocation motion. The two configurations differ only in the orientation of the applied tensile load relative to that of the laths — either perpendicular or at 45$°$. In the latter case, slip along the so-called habit plane results in localized plastic deformation, while the former results in a more diffuse activation of plasticity. Insights obtained based on the idealized cases are used to formulate a three-dimensional constitutive model which captures both deformation mechanisms. The model is applied to microtensile tests of single-packet lath martensite samples. It is shown that the orientation-dependent heterogeneity is accurately captured by the two deformation mechanisms accounted for by the model.

Double-network (DN) gels possess exceptional mechanical properties and hold great promise as innovative soft materials due to their peculiar inherent structure made of a first highly cross-linked brittle short-chain network and a second flexible loosely cross-linked long-chain network. The stretch-induced molecular ordering in DN gels causes anisotropic effects along with complex interactions between the two networks. This paper attempts to contribute to the understanding of the history-dependent anisotropic multiaxial damage behavior of DN gels. A multiscale model is formulated for the constitutive description of the internal network physics in DN gels, such as the stretch-induced molecular ordering and damage, in connection to their multiaxial mechanics. The scission mechanism in the short-chain network is considered at the chain-scale using statistical mechanics by treating the breakage of internal molecular bonds as an energy activation process related to the thermal oscillation and stimulated by the chain stretch. The transition scale microsphere-based method is employed to realize the transition from the short-chain scale to the network scale while considering the statistical variability in chain lengths and their evolution due to the chain rearrangement consecutive to the progressive chain scission events. A two-phase microstructure representation allows accounting for the presence of the superimposed long-chain network along with the effective coupling due to mutual interpenetration of the two networks. The model capabilities to capture the biaxial behavior of gel material systems are critically evaluated by comparing the model outputs with a few available experimental observations under various loading modes highlighting both internal network coupling and anisotropic damage. The relevance of the proposed approach is highlighted by the favorable alignment of the model simulations with experimental observations of gel systems subjected to uniaxial stretching along orthogonal directions and exhibiting history-dependent anisotropic features induced by prior biaxial loading. The damage and rearrangement micro-mechanisms are discussed with respect to the model in connection to loading history.

The present study focuses on further extensions of the more general three-parameter Weibull distribution to describe the statistical scatter of fracture toughness values and to evaluate the characteristic toughness of structural steels using a statistical description of toughness data in comparison with the minimum of three equivalent (MOTE) method. Fracture toughness tests conducted on several types of structural steels, including an ultra high strength steel and pressure vessel steels, provide the experimental data upon which the Weibull statistical analyses are conducted. These analyses compare descriptions of fracture toughness values based on a standard three-parameter Weibull function with fixed values for parameters $\alpha$ and $K_{min}$, and a general three-parameter Weibull distribution with unknown parameters $(\alpha ,K_0,K_{min})$ in connection with a goodness-of-fit method to assess how well the experimental data fits the assumed distribution. Further, the study also shows that use of a fixed percentile of the distribution describing the toughness data set provides more consistent values of characteristic toughness compared to the MOTE procedure.

The partial-slip contact at nano-scale is always influenced by a surface effect. A new model based on the Gurtin-Murdoch (G-M) surface elasticity theory is proposed in this paper to study the partial-slip contact behavior of a rigid flat nano-indenter on an elastic half-space. The surface effect in the partial-slip contact is characterized via a non-classical boundary condition involving a surface-induced normal traction related to the residual surface stress and a surface-induced tangential traction related to the surface elasticity, the influences of which on stress and displacement fields and the stick-slip state at the contact surface are investigated. It is found that, with the increase of residual surface stress, both the normal pressure and vertical and horizontal displacements in the contact zone decrease, the relative slip between indenter and substrate reduces and the stick region is enlarged. Such effects are basically attributed to the action of the surface-induced normal traction opposite to the externally applied compression. However, the increase of surface elastic constants is conductive to the relative slip and results in a shrinkage of the stick region, which is attributed to the action of the surface-induced tangential traction opposite to the frictional stress. An interesting phenomenon is further unveiled that, when the frictional coefficient increases, the dominant role in affecting the stick-slip state changes from the surface-induced tangential traction to the normal one, thus inspiring a feasible route to manipulate the surface effect by tuning the frictional coefficient of substrate. The present research enables one to better understand the partial-slip contact behavior of nano-indenters, which is of guiding value for anti-wear designs in nano-mechanical devices.

Let Sym${}_0$ be the space of traceless symmetric second-order tensors. We say that a polycrystalline elastic–plastic material is weakly-textured if its yield function $f:{\text{Sym}}_0\to R$ is the sum of a texture-independent isotropic part $f_{\text{iso}}$ and an anisotropic part which is linear in the relevant texture coefficients. Let $c>0$ and $S≔f^{-1}\left(c\right)\subset {\text{Sym}}_0$ be the yield surface of the weakly-textured material in question. We present a sufficient condition (*), namely that ${\nabla }^{2}f\left(S\right)$ be positive definite for each $S\in S$, for a smooth yield surface $S$ to be strictly convex in Sym${}_0$. We apply this sufficient condition to weakly-textured materials with yield functions that satisfy the following conditions: (i) the yield functions $f$ and $f_{\text{iso}}$ are smooth; (ii) ${\nabla }^2{f}_{\text{iso}}\left(S\right)$ is positive definite for each $S$ in $S_{\text{iso}}≔f_{\text{iso}}^{-1}\left(c\right)\subset {\text{Sym}}_0$. We prove that the yield surface $S\subset {\text{Sym}}_0$ of such weakly-textured material is strictly convex if the texture coefficients in $f$ are sufficiently small. As illustration for practical applications, by appealing to condition (*) we study the strict convexity of the yield surface pertaining to a weakly-textured orthorhombic aggregate of cubic crystallites which has a quadratic yield function of the type proposed by Hill in 1948.