Macroscopic Deformation Modes Research Articles

Meso-scale deformation and strength mobilization mechanisms of EPS composite soil

Expanded polystyrene (EPS) composite soil is composed of two solid constituents (cemented soil and EPS beads), which together with the inter-constituent interfaces form a unique mesoscopic structure. The macroscopic behavior of EPS composite soil has been widely investigated so far, but the focus has seldom been put on the meso-scale mechanisms behind the macroscopic deformation features and strength mobilization processes. In this study, systematic experiments and refined numerical simulations are utilized to examine the meso-scale mechanical responses of EPS composite soil under triaxial compression to reveal the associated mechanisms. Here, meso-scale is a scale smaller than a sample scale but larger than an EPS bead scale. First, the mechanical behavior of cemented soil, EPS material and their interface is obtained in experiments; their constitutive models are formulated, and the model parameters are calibrated based on experimental results. Then, experiments and refined numerical simulations of triaxial compression on EPS composite soil are performed. It is found that the rich macroscopic mechanical behavior of EPS composite soil has a mechanical source (contrast in mechanical behavior between EPS and cemented soil) and a geometric source (non-uniform distribution of EPS beads). The mechanical source leads to highly non-uniform stress and strain distributions within an EPS composite soil. The geometric source causes strain localization in zones with local concentration of EPS beads, leading to three macroscopic deformation modes, i.e., overall shear localization, local lateral expansion, and overall uniform expansion. In strength mobilization, cemented soil matrix first mobilizes its strength because it takes most of the load and contributes much to deformation at the early stage of triaxial compression. EPS beads are later progressively involved in the overall load bearing and deformation of the EPS composite soil sample. EPS beads make more contribution to stress than to strain due to its soft nature.

Enhancing specific energy absorption of additively manufactured titanium lattice structures through simultaneous manipulation of architecture and constituent material

Titanium lattice structures have found a wide range of lightweight applications. However, lattice structures made from the commonly-used commercially pure titanium (CP−Ti) and Ti−6Al−4V exhibit either low strength or post-yielding softening/collapse under uniaxial compression, making them less attractive to energy absorbing applications. In the present work, a series of titanium gyroid lattice structures have been designed and additively manufactured by laser powder bed fusion ( L -PBF) to enhance the specific energy absorption (SEA) through manipulation of the architecture and the constituent material. Experimental results show that tailoring the sheet thickness gradient of gyroid lattice structures enables the transformation of the macroscopic deformation mode from hardening followed by softening, which is commonly seen in lattice structures, to continuous hardening. The addition of MgO nanoparticles to CP−Ti feedstock further improves the yield strength through oxygen solute strengthening, while maintaining the continuous hardening behaviour without any post-yielding softening or collapse. As a result, when both sheet thickness gradient and MgO are introduced, the SEA of the uniform gyroid lattice structure is enhanced by approximately 63% due to the combination of continuous hardening behaviour and high strength. Finite element analysis based on the modified volumetric hardening model has been performed to shed light on the underlying mechanism that governs the continuous hardening behaviour. This study demonstrates the tremendous potential of marrying architecture engineering with material design to create high performance lightweight lattice structures by L -PBF.

The in-plane dynamic crushing of quadrilateral chiral honeycomb coatings

For the anti-impact performance of hyperelastic coatings covered on the ship hull, the in-plane dynamic crushing behaviors of quadrilateral chiral honeycomb coatings (including chiral and anti-chiral) were numerically studied by explicit dynamic finite element simulations. The deformation mode, energy absorption and supporting reaction force under different impact speeds have been analyzed. The results show that: (1) If the impact speed is low, the chiral honeycomb coatings display the rotational deformation; (2) With the increase of impact speed, the deformation at the top of coating is remarkable; (3) The response of energy absorption and supporting reaction force corresponds to the macroscopic deformation mode of chiral honeycomb coatings.

Failure criteria for porous dome rocks and lavas: a study of Mt. Unzen, Japan

Abstract. The strength and macroscopic deformation mode (brittle vs. ductile) of rocks is generally related to the porosity and pressure conditions, with occasional considerations of strain rate. At high temperature, molten rocks abide by Maxwell's viscoelasticity and their deformation mode is generally defined by strain rate or reciprocally by comparing the relaxation timescale of the material (for a given condition) to the observation timescale – a dimensionless ratio known as the Deborah (De) number. Volcanic materials are extremely heterogeneous, with variable concentrations of crystals, glass–melt, and vesicles (of different sizes), and a complete description of the conditions leading to flow or rupture as a function of temperature, stress and strain rate (or timescale of observation) eludes us. Here, we examined the conditions which lead to the macroscopic failure of variably vesicular (0.09–0.35), crystal-rich (∼ 75 vol %), pristine and altered dome rocks (at ambient temperature) and lavas (at 900 °C) from Mt. Unzen volcano, Japan. We found that the strength of the dome rocks decreases with porosity and is commonly independent of strain rate; when comparing pristine and altered rocks, we found that the precipitation of secondary mineral phases in the original pore space caused minor strengthening. The strength of the lavas (at 900 °C) also decreases with porosity. Importantly, the results demonstrate that these dome rocks are weaker at ambient temperatures than when heated and deformed at 900 °C (for a given strain rate resulting in brittle behaviour). Thermal stressing (by heating and cooling a rock up to 900 °C at a rate of 4 °C min−1, before testing its strength at ambient temperature) was found not to affect the strength of rocks.In the magmatic state (900 °C), the rheology of the dome lavas is strongly strain rate dependent. Under conditions of low experimental strain rate (≤ 10−4 s−1), ductile deformation dominated (i.e. the material sustained substantial, pervasive deformation) and displayed a non-Newtonian shear thinning behaviour. In this regime, the apparent viscosities of the dome lavas were found to be essentially equivalent, independent of vesicularity, likely due to the lack of pore pressurisation and efficient pore collapse during shear. At high experimental strain rates ( ≥ 10−4 s−1) the lavas displayed an increasingly brittle response (i.e. deformation resulted in failure along localised faults); we observed an increase in strength and a decrease in strain to failure as a function of strain rate. To constrain the conditions leading to failure of the lavas, we analysed and compared the critical Deborah number at failure (Dec) of these lavas to that of pure melt (Demelt = 10−3–10−2; Webb and Dingwell, 1990). We found that the presence of crystals decreases Dec to between 6.6×10−4 and 1×10−4. The vesicularity (φ), which dictates the strength of lavas, further controls Dec following a linear trend. We discuss the implications of these findings for the case of magma ascent and lava dome structural stability.

Smooth-shell metamaterials of cubic symmetry: Anisotropic elasticity, yield strength and specific energy absorption

Shell-lattices consist of a single, periodic, non-intersecting shell of uniform wall thickness that separates two intertwined void phases. To obtain a comprehensive overview on their small and large strain response, three families of shell-lattices are derived from Simple-Cubic (SC), Face-Centered Cubic (FCC) and Body-Centered Cubic (BCC) tube-lattices using a parameterized surface-smoothening functional. Each family's central element is an approximation of a Triply Periodic Minimal Surface (TPMS). Detailed finite element simulations are carried out for more than 800 shell-lattices covering relative densities ranging from 1% to 80%. It is found that the TMPS-like structures exhibit highly anisotropic elastic and plastic properties that depend on the type of cubic symmetry. However, when averaging the mechanical properties over all possible directions of loading, the performance of the SC, FCC and BCC shell-lattices turns out to be similar, with all structures providing substantially higher stiffness and strength than optimal truss-lattices of equal mass. They also exhibit high specific energy absorption for large strain compression. It is found that the macroscopic deformation mode changes from foam-like crushing (for relative densities below 10%) to bulk-like positive strain hardening (for relative densities above 20%). The spectrum of anisotropic structures obtained through varying the bias parameter of the surface-defining functional also includes elastically-isotropic shell-lattices. The Young's modulus of the isotropic shell-lattices of FCC and BCC symmetry is slightly higher than the average modulus of their TPMS-like counterparts, while the opposite holds true for SC structures. Compression experiments are performed on additively-manufactured stainless steel 316L specimens to validate the conclusions drawn from numerical simulations.

Consistent multiscale analysis of heterogeneous thin plates with smoothed quadratic Hermite triangular elements

A consistent multiscale formulation is presented for the bending analysis of heterogeneous thin plate structures containing three dimensional reinforcements with in-plane periodicity. A multiscale asymptotic expansion of the displacement field is proposed to represent the in-plane periodicity, in which the microscopic and macroscopic thickness coordinates are set to be identical. This multiscale displacement expansion yields a local three dimensional unit cell problem and a global homogenized thin plate problem. The local unit cell problem is discretized with the tri-linear hexahedral elements to extract the homogenized material properties. The characteristic macroscopic deformation modes corresponding to the in-plane membrane deformations and out of plane bending deformations are discussed in detail. Thereafter the homogenized material properties are employed for the analysis of global homogenized thin plate with a smoothed quadratic Hermite triangular element formulation. The quadratic Hermite triangular element provides a complete C1 approximation that is very desirable for thin plate modeling. Meanwhile, it corresponds to the constant strain triangle element and is able to reproduce a simple piecewise constant curvature field. Thus a unified numerical implementation for thin plate analysis can be conveniently realized using the triangular elements with discretization flexibility. The curvature smoothing operation is further introduced to improve the accuracy of the quadratic Hermite triangular element. The effectiveness of the proposed methodology is demonstrated through numerical examples.

Directionality of slip traces and banded structures in fcc materials processed by equal-channel angular extrusion

A statistical analysis of the directionality of slip traces in face-centered cubic crystals processed by a single pass of equal-channel angular extrusion was conducted based on crystal plasticity simulations. The slip traces are found to orient along various directions on each of the inspection planes, indicating a strong grain-orientation dependency. The slip traces depict preferred alignment directions that coincide with those of banded structures found in the literature and can be traced to the macroscopic deformation mode.

Kinetic Monte Carlo study of activated states and correlated shear-transformation-zone activity during the deformation of an amorphous metal

Shear transformation zone (STZ) dynamics simulations, which are based on the kinetic Monte Carlo algorithm, are used to model the mechanical response of amorphous metals and provide insight into the collective aspects of the microscopic events underlying deformation. The present analysis details the activated states of STZs in such a model, as well as the statistics of their activation and how these are affected by imposed conditions of stress and temperature. The analysis sheds light on the spatial and temporal correlations between the individual STZ activations that lead to different macroscopic modes of deformation. Three basic STZ correlation behaviors are observed: uncorrelated activity, nearest-neighbor correlation, and self-reactivating STZs. These three behaviors correspond well with the macroscopic deformation modes of homogeneous flow, inhomogeneous deformation, and elastic behavior, respectively. The effect of pre-existing stresses in the simulation cell is also studied and found to have a homogenizing effect on STZ correlations, suppressing the tendency for localization.

Flow serration in a Zr-based bulk metallic glass in compression at low strain rates

It is demonstrated that at slow strain rates (∼10 −4 s −1) in compression, the dominant room temperature macroscopic deformation mode in a ductile Zr-based bulk metallic glass is single shear along the principal shear plane. The stress–strain curve exhibited serrated flow in the plastic region. Scanning electron micrographs of the deformed samples revealed regularly spaced striations on the shear surface. A detailed analysis of the observed serrations disclosed that they were intimately related to the striations on the shear surface, suggesting that the serrations were mainly caused by intermittent sample sliding. Further investigations were conducted using in situ compression experiments; video images showed that there was indeed a one-to-one correspondence between the intermittent sliding and flow serration. The current study therefore suggests that flow serration is a result of intermittent sample sliding. This result also implies that the principal shear plane, once formed, is the preferential site for additional shear band formation.

Deformation in metals after low-temperature irradiation: Part I – Mapping macroscopic deformation modes on true stress–dose plane

Macroscopic deformation modes, elastic, uniform plastic, and unstable plastic deformation modes, are mapped in tensile true stress–dose space for more than two dozen metallic materials consisting of 13 body-centered cubic (bcc), 11 face-centered cubic (fcc), and two hexagonal closed packed (hcp) metals. The boundaries between different deformation zones are set by the true stress versus dose curves: the yield stress (YS), plastic instability stress (PIS), and true fracture stress (FS) plotted as functions of dose. Values for these true stresses are obtained from uniaxial tensile tests or calculated from engineering tensile data using a linear strain-hardening model for necking deformation. The relatively low-strength annealed fcc metals display large uniform plasticity regions, while unstable deformation regions are dominant in the harder bcc and hcp metals. PIS values for all materials are independent of dose except for the precipitation-hardened IN718 alloy, where a decrease of PIS occurs due to an irradiation-induced change in second phases. In the bcc materials for high-temperature application, such as 9Cr ferritic/martensitic steels, sintered molybdenum, vanadium, and tantalum, the radiation-induced embrittlement is characterized in terms of FS decreasing with dose at relatively high doses. FS is nearly dose-independent below the critical dose for embrittlement. It is concluded that the tensile stress-based deformation mode maps effectively integrate mechanical property information and characterize differences in radiation effects between crystalline structures or material groups.

Dislocation structures. Part II. Slip system dependence

Part I established, via extensive transmission electron microscopy investigations, that the type of dislocation structure formed in metals of medium-to-high stacking fault energy upon deformation in tension or rolling to moderate strain levels (≤0.8) depends strongly on crystallographic grain orientation. This paper analyzes the grain orientation-dependent structures in terms of the active slip systems, focusing on the crystallographic plane of extended planar boundaries (geometrically necessary boundaries). The analysis establishes slip systems as the factor controlling the dislocation structure. Five fundamental slip classes, consisting of one to three active slip systems, have been identified. Multiple activation of these slip classes is also considered. The slip classes give rise to different types of dislocation structure, of which all except one contains geometrically necessary planar boundaries aligning with unique crystallographic planes (not necessarily slip planes). A slip class leads to the same type of structure, irrespective of the macroscopic deformation mode, as also demonstrated by successful predictions for shear deformation.

Deformation mode map of irradiated 316 stainless steel in true stress–dose space

Microscopic and macroscopic deformation modes in type 316 stainless steels after low-temperature irradiation have been mapped into the true stress–dose coordinate system. This paper defines and explains the deformation modes in 316 and 316LN stainless steels and suggests the procedures to produce a deformation mode map. A variety of microstructural features such as dislocation tangles and pileups, dislocation channels, stacking faults, and twins have been observed in the deformation of irradiated stainless steels. Attempts were also made to depict macroscopic phenomena such as uniform deformation, necking, and final fracture in the map. Stress criteria for twinning, channeling, plastic instability, and final failure were proposed and used to establish boundaries between the different deformation modes. Two alternative strain localization mechanisms, twinning and channeling, shared the high-dose region. The region of stable plastic deformation became narrower as dose increased, while the elastic deformation region was enlarged with dose and the unstable deformation region was kept unchanged over the whole dose range.

Compressive properties of lotus-type porous stainless steel

Lotus-type porous stainless steel (SUS304L), possessing cylindrical pores aligned in one direction, was fabricated by means of a continuous zone melting technique undera pressurized hydrogen/helium atmosphere. Compression tests were carried out on the resultant lotus stainless steel not only in the directions parallel and perpendicular tothe elongated-pore direction but also in other directions to reveal its anisotropic compressive behavior. The macroscopic deformation modes depend on porosity and the angle between the elongated-pore direction and compression direction, which is a unique characteristic resulting from its anisotropic porous structure. The yield stress in the pore direction decreases almost linearly with increasing porosity, while that in the perpendicular direction decreases more rapidly. The yield stress in the direction of θ from the elongated-pore direction decreases monotonically with increase in θ. The yield behavior of lotus stainless steel was described using micromechanical mean-field theory.

Boundary characteristics in Heavily Deformed Metals

The potential of creating nanostructured metals by plastic deformation to very high strains is currently the subject of intensive research. An important part of this research concerns evolution of the characteristics of deformation induced boundaries, in particular boundary spacing and boundary misorientation. The aim of this paper is to give an overview of the present understanding of the relations between these characteristics, the microscopic deformation mechanisms and the macroscopic deformation mode.

Simulation of sheet metal forming using explicit finite element techniques: effect of material and forming characteristics: Part 2. Deep-drawing of square cups

The simulation of the deep-drawing of square cups of coated galvanised steels using the explicit non-linear finite-element (FE) code DYNA-3D is reported. Based on the extensive verification procedure of the FE model regarding the selection of the suitable material and processing characteristics, described in detail in a companion paper for deep-drawing of axisymmetric cylindrical cups of the same materials, upper and lower limits of the simulated parameters are defined, bracketing, therefore, any optimal parametric prediction. The evaluation of the CPU time cost and comparisons between simulated values and experimentally predicted values, regarding strain distributions, punch load/punch travel curves and macroscopic deformation modes, which are in good agreement, indicate that the proposed model, under the assumptions and limitations made, well predicts the forming behaviour of deep-drawn components of various geometries.

Simulation of sheet metal forming using explicit finite-element techniques: effect of material and forming characteristics: Part 1. Deep-drawing of cylindrical cups

The use of the explicit non-linear finite element (FE) code DYNA 3D in sheet metal forming simulation is examined. A 3D FE model for the deep-drawing of cylindrical cups was constructed and the simulation results obtained using different simulation parameters, i.e. punch velocity, sheet material density, Coulomb friction coefficient at the tool–blank interfaces and type and dimensions of the FE mesh-elements, compared with experimental results regarding strain distributions (radial, circumferential and thickness through the sheet) and punch force–punch travel curves carried out on five galvanised steels and an aluminium sheet, for three different geometries of axisymmetric cup: Good agreement was obtained. The evaluation of the CPU time cost, the macroscopic deformation modes, the strain distributions of the deformed material and the process characteristics obtained for the constructed FE models, was directed towards the selection of the most efficient material and punch parameters. Finally, an attempt was made to construct rules from the above-mentioned verification, which may be used for reliable sheet metal forming simulations, using explicit finite-element codes.

Shear band formation and cracking of a metallic glass irradiated with high energy laser pulses

A concentric deformation pattern, shear bands and cracks are produced in Fe80B14.8Si3.5C2 glass, irradiated with 12 msec duration ruby laser pulses, ranging in power densities between 105 and 107 W cm−2. This deformation front propagates through a steep temperature gradient and a partially crystallized heat-affected zone, giving rise to variations of the macroscopic deformation mode as a function of radial distance from the centre of the laser spot. For the first time, a direct experimental mapping of crack tip plasticity, in the form of an elliptical shear band zone, has been recorded. A theoretical model, which predicts such a shear band zone at the crack tip, is used to discuss the elastic-plastic response of the metallic glass.