Undergoing Plastic Flow Research Articles

Ultra-strong and ductile amorphous-crystalline Ti-Zr-Hf-Nb-Ta/Co-Ni-V nanolaminate thin films

Films with a combination of high strength, large ductility, and high thermodynamic stability are always pursued for industrial applications. Here, we prepared the amorphous-crystalline Ti-Zr-Hf-Nb-Ta/Co-Ni-V nanolaminate with hardness and yield strength of 7.4 GPa and 3.8 GPa, and large deformability of ∼70%. The ductility is attributed to two aspects. One is the Ti-Zr-Hf-Nb-Ta/Co-Ni-V layer interfaces acted as barriers to obstruct the propagation of nanocracks at the heavily deformed stage. Another is that amorphous layers acted as dislocation sinks promoting the dislocations to get annihilated when undergoing plastic flow, maintaining the plastic deformability of the crystalline layers. After annealing at 873 K for 1 h, the Co-Ni-V layer changes to a V-rich amorphous layer with minor nanocrystals, while the Ti-Zr-Hf-Nb-Ta layer transforms to a Ni-rich amorphous layer, due to the diffusion of Co and Ni. This chemical partitioning and consequent amorphization lead to the enhanced hardness and yield strength of 9.4 GPa and 4.5 GPa, but low ductility. In addition, the microstructure and mechanical properties of the nanolaminate can be further optimized by adjusting substrate temperature, layer thickness, and annealing process. The findings provide a new avenue for improving the mechanical properties of nanolaminates in a controllable manner.

Numerical Simulation Research on Rotating Band Dynamic Engraving Process of CTA Artillery

In order to study the mechanical mechanism of the dynamic engraving process of the CTA band, the simulation model of the engraving process is established considering the friction and contact characteristics between the interfaces. The adaptive FEM-SPH coupling algorithm is used to obtain the variation law of the temperature and stress distribution of the band, the attitude of the projectile, and the dynamic engraving resistance through numerical calculation. The results show that the band undergoes plastic flow during engraving, and the surface temperature of the band is close to the melting point temperature of the material during the adiabatic engraving. The engraving process presents obvious segmented characteristics, and the initial engraving speed has an important influence on the spatial projectile attitude. The variation of dynamic engraving resistance is quite different from that of the quasi-static model, and the resistance has two ‘rising-decreasing’ processes.

Non-Quadratic Pseudo Dual Potentials for Plastic Flow Modeling

The existence of dual flow potentials is well established in mathematical theory of plasticity since the seminal work by Hill in 1987. For a metal undergoing plastic flow, a flow stress potential is used to compute its plastic strain increments when the applied yield stress is known. On the other hand, the corresponding dual flow strain-rate potential is used to compute the stress on the flow surface when the plastic strain increments are given. This work examines some issues associated with plasticity modeling using non-quadratic dual flow potentials. Unlike the quadratic case where flow stress and strain-rate potentials are the exact dual to each other, it is often difficult if not impossible to obtain analytically the dual of a non-quadratic flow stress or strain-rate potential. The study instead focuses on formulating and assessing various non-quadratic pseudo dual flow potentials that approximate the actual flow surfaces in either stress or strain-rate space. The difference and connection between the yield surface and flow surface in non-associated plasticity are also investigated. Although only one of the dual flow potentials is actually needed for their applications in associated and non-associated plasticity modeling, the unique advantage of having both dual flow potentials on hand even in their pseudo forms is pointed out for new computational analyses.

Polystyrene Glasses under Compression: Ductile and Brittle Responses.

Polystyrene of different molecular weights and their binary mixtures are studied in terms of their various mechanical responses to uniaxial compression at different temperatures. PS of Mw = 25 kg/mol is completely brittle until it is above its glass transition temperature Tg. In contrast, upon incorporation of a high molecular weight component, PS mixtures turn from barely ductile a few degrees below its Tg to ductile over 40° below Tg. In the upper limit, a PS of Mw = 319 kg/mol yields and undergoes plastic flow, even at T = -70 °C. The observed dependence of mechanical responses on molecular weight and molecular weight distribution can be adequately rationalized by the idea that yielding and plastic compression are caused by chain networking.

Parametric Analyses of the Mixed-Lubrication Performance of Rolling/Sliding Contacts in High-Load and High-Speed Conditions

This article conducts a theoretical analysis of the mixed lubrication rolling/sliding contacts using a recently developed mathematical model that incorporates asperity-level mechanical, thermal, and tribochemical aspects into the bulk elastohydrodynamic setting. A systematic parametric analysis is carried out to study the mixed lubrication in high-load, high-sliding conditions. The parameters studied include contact size, surface roughness, surface hardness, surface boundary film property, and operating load and speed. The performance and the state of contact and lubrication of the system are measured by load sharing between fluid and solid, area of asperity contacts, fraction area of asperity contacts undergoing plastic flow, as well as experimentally measurable variables such as traction coefficient, friction power intensity, and temperature of the contact. The results show that the surface roughness, surface hardness, load, and sliding velocity are very important parameters affecting the state and severity of the mixed lubrication. The results also suggest that there may be an optimal range of surface hardness to achieve the best performance. A hardness that is too low is vulnerable to mechanical stress–induced plastic deformation, whereas a hardness that is too high may cause thermal stress–induced surface distress in high sliding. The authors hope that the model and the theoretical approach can be used in conjunction with experiments to gain more fundamental insights into the performance and failure of high-load, high-speed rolling/sliding contacts in mixed lubrication.

A Mathematical Model for the Mixed Lubrication of Non-Conformable Contacts With Asperity Friction, Plastic Deformation, Flash Temperature, and Tribo-Chemistry

A mathematical model is presented in this paper for rolling-sliding contacts operating in a mixed regime of elastohydrodynamic lubrication and boundary lubrication. The model is based on the framework of Johnson et al. (1972, “A Simple Theory of Asperity Contacts in Elastohydrodynamic Lubrication,” Wear, 19, pp. 91–108). It incorporates into this framework a number of important asperity-level variables including asperity friction, friction-induced plastic flow, flash temperature, and boundary-film tribo-chemistry. The model yields a number of variables useful for the assessment of the state of the mixed lubrication. They include the load sharing between fluid and asperities, area of asperity contacts, and fraction area of asperity contacts undergoing plastic flow along with experimentally measurable variables such as the traction coefficient, friction power intensity, and temperature of the overall contact. The model is limited to mixed-lubrication problems in which the load is mainly carried by the fluid pressure and the total area of asperity contacts is a small percentage of the Hertz area. Further development is possible to formulate a model into a wider mixed-lubrication regime using some modeling concepts developed in this paper in conjunction with other modeling techniques.

Neutron Diffraction Measurement of Stress Redistribution in Parallel Seven-Wire Strands after Local Fracture

We report results from neutron diffraction experiments where partitioning of applied tensile load between the inner and outer wires of seven-wire parallel and quasi-parallel wire strands were measured while 1-all wires were undergoing elastic deformation, 2-where one wire within the bundle was undergoing plastic flow and, 3-when one or more wires fractured under load. The results indicate that mechanical interference and friction mechanisms have similar contributions to the load transferred to fractured wires, and both mechanisms should be included in analytical or numerical formulations of strain partitioning in quasi-parallel wire cables.

SPM oxidation and parallel writing on zirconium nitride thin films

Systematic investigation of the SPM oxidation process of sputter-deposited ZrN thin films is reported. During the intrinsic part of the oxidation, the density of the oxide increases until the total oxide thickness is approximately twice the feature height. Further oxide growth is sustainable as the system undergoes plastic flow followed by delamination from the ZrN–silicon interface keeping the oxide density constant. ZrN exhibits superdiffusive oxidation kinetics in these single tip SPM studies. We extend this work to the fabrication of parallel oxide patterns 70 nm in height covering areas in the square centimeter range. This simple, quick, and well-controlled parallel nanolithographic technique has great potential for biomedical template fabrication.

A p-adaptive scheme for overcoming volumetric locking during plastic flow

A feature of many classical plasticity yield functions is that they impose a volumetric constraint on plastic deformation. For low-order finite elements, this results in kinematic restraints on possible deformation modes of an element leading to an overly stiff response. The most robust procedure for overcoming volumetric locking is to use higher-order finite elements. However, low-order elements are popular for their efficiency and simplicity. To remedy volumetric locking in low-order elements, a p-adaptive scheme is proposed where through the partition of unity property of finite element shape functions, the underlying basis of low-order finite elements undergoing plastic flow is enhanced with higher-order polynomial functions. The computational result is extra degrees of freedom at existing nodes of elements undergoing plastic flow, while the rest of the nodes remain unaltered. The performance of the scheme is illustrated through two- and three-dimensional numerical examples.

Enhanced Case-II diffusion of diluents into glassy polymers undergoing plastic flow

Dramatic enhancement of diluent conductance in glassy polymers actively undergoing plastic flow has long been suspected. We report observations of this phenomenon in a glassy poly(ether imide) (Ultem)™ in the presence of resorcinol bis(diphenyl phosphate) (RDP) by means of the limited-supply diffusion experiment developed earlier by Nealey et al. In this experiment it is demonstrated that RDP uptake in plastically deforming Ultem is nearly identical at 113°C, ie. 102°C below Tg, as it is at 215°C, at Tg, without concurrent plastic flow. While the characteristic profiles of penetrating Case-II fronts are present in experiments at 130°C without plastic flow, they are absent in experiments above Tg without plastic flow and in those at 113°C undergoing concurrent plastic flow. This demonstrates that in the plastically deforming polymer, well below Tg, a steady dilated flow state exists, which resembles in its molecular level conformational rearrangements that at Tg without deformation, where in both the resistance to diluent penetration has been radically reduced. Based on the measured diffusion constant of RDP in Ultem, the structural correspondence of the thermally dilated state at Tg and the flow dilated state at 113°C is equivalent to an increase of the diffusion constant by a factor of 1.9×104 in the latter.

Theoretical calculation of the stress-strain behavior of dual-phase metals with randomly oriented spheroidal inclusions

A simple model is developed to determine the overall response of dual-phase metals with an inclusion/matrix microgeometry. The inclusions are taken to be spheroidal in shape and are randomly oriented and homogeneously dispersed in the matrix. No restriction is placed on whether the inclusions are harder or softer (in the sense of flow stress) than the matrix, and as with most dual-phase metals, both phases are capable of undergoing plastic flow. The yielding process of the inclusions is now orientation dependent and sequential, and the overall elastoplastic response of the two-phase system is found to be strongly dependent upon the inclusion shape and concentration, even more so than on the corresponding elastic behavior. Disc-shaped inclusions generally give a superior reinforcing effect when the matrix is the softer phase, whereas spherical inclusions are more effective when the matrix is the harder one. As compared to the condition when the inclusions are strictly elastic, the plasticity of inclusions is found to translate into noticeable reduction in the flow stress of the composite. Comparison of the theoretical prediction with the experimental data for a ferrite/austenite system further shows a reasonable agreement.

The overall elastoplastic stress-strain relations of dual-phase metals

T wo simple, albeit approximate, theories are developed to estimate the stress-strain relations of dual-phase metals of the inclusion-matrix type, where both phases are capable of undergoing plastic flow. The first one is based upon Hill's recognition of a weakening constraint power in a plastically deforming matrix, whereas the second one is based on Kröner's elastic constraint in the treatment of the single inclusion-matrix interaction. The inclusion-inclusion interaction at finite concentration is accounted for by the Mori-Tanaka method in both cases. Consistent with the known elastic behavior, the first theory discloses that the geometrical arrangement of the constituents has a significant influence on the overall elastoplastic response. When the harder phase takes the position of the matrix the composite is far Stiffer than that when it takes the position of inclusions. The strong elastic constraint associated with the second theory tends to provide an upper-bound type of estimate regardless of whether the matrix is the harder phase or the softer, and, therefore, it is suggested that this theory be used only for the class of composites whose matrix is the harder phase. Both theories are finally applied to predict the stress-strain relations of dual-phase stainless steels, and the results are found to be in satisfactory agreement with the test data.

Plastic instabilities: Implications for the origin of intermediate and deep focus earthquakes

Adiabatic or catastrophic plastic shear has been reported in metals, polymers, and metallic glasses. The phenomenon is associated with rapid stress drops and audible pings or clicks as the material deforms in a plastic manner. The driving force for the plastic instability is the stored elastic strain energy of the loading system, and in many respects the behavior is reminiscent of the shear stress response arising from stick slip events during unstable frictional sliding, although the precise mechanism is different. It is shown here that adiabatic plastic shear is capable of explaining the detailed distribution of intermediate and deep focus earthquakes within subduction zones, the earthquake events being the result of instabilities in material undergoing plastic flow. It is argued that for a particular strain rate there exists a critical temperature, TC, which is depth dependent; for temperatures below TC the material is strain rate softening and, for a soft enough loading system, may undergo catastrophic plastic shear. For temperatures above TC the material is strain rate hardening and is always stable during plastic shear. The cutoff depth for deep focus earthquakes then corresponds to the transition from strain rate softening to strain rate hardening material, and for commonly accepted geothermal gradients within the slab corresponds to approximately 800 km. The precise distribution of earthquakes within the slab is a function of the subtle interplay between the geothermal gradient and the TC gradient. In particular, a decrease in seismic activity is to be expected below about 300 km in the slab with total stress drops decreasing from a maximum of 700 MPa above 300 km to a maximum of ≈ 50 MPa below 300 km. The differences in foci distribution between subduction zones such as Tonga, New Hebrides, and Peru result from minor differences in the geothermal gradients within the slabs. The model predicts the development of triple seismic zones high in the slab, double seismic zones down to approximately 300 km, and single seismic zones down to ≈ 800 km. Such a distribution is to be expected of relatively young, cool slabs; as the slab heats up, the seismic activity retreats up the slab. The paper only proposes a deformation mechanism for earthquake generation, it does not address the stress field within the slab but only the distribution of strength. Thus the distribution of focal plane mechanisms is not considered, only the locations where earthquakes due to plastic instabilities are possible. The absence of earthquakes does not necessarily mean that the slab does not exist, it only means that the slab is too hot to undergo plastic instability. This means that aseismic subduction is a distinct possibility in many regions of high geothermal gradient within the slab (i.e. > circa 3°C km−1).

Void collapse and void growth in crystalline solids

The problem of large deformation and eventual collapse (or growth to a final shape, depending on the microstructure and loading) of voids in a crystalline solid which undergoes plastic flow by slip on crystallographic planes is considered and solved analytically for plane problems, using certain reasonable simplifying assumptions. It is shown that because of local anisotropic plastic flow, an initially circular (in two dimensions or spherical in three dimensions) void quickly deforms into a noncircular (or nonspherical) shape, even under all-around uniform far-field pressure or tension. Using an incremental solution, the shape of the void at each loading stage is approximated by an equivalent ellipse, and this procedure is continued until either the void collapses into a crack (which occurs always under compression and in special cases even under tension) or attains a constant aspect ratio (under tension only). The residual stresses in the vicinity of the collapsing void are calculated and used to establish whether or not the crack which is formed by the void collapse will continue to grow upon the release of the overall uniform compressive loads. It is shown that this depends on the initial void size, on the ductility of the material, as well as on the rate of the loading which affects the ductility. The mechanism of possible overall failure caused by void collapse under far-field compressive loads and possible subsequent crack growth upon unloading is studied, using power-law rate-dependent plastic slip and experimental results on flow stress under shock loading. Results are compared with experimental observations, arriving at good agreement. In particular, the important effect of the loading rate on void collapse and subsequent failure mode is illustrated. Furthermore, the void growth processes under simple shear and tensile loading are investigated, and it is shown that, depending on the far-field loading condition and the microstructure, a void may grow by self-similar expansion or it may collapse into a crack. The mechanisms of void deformation under various loading conditions are illustrated.

Reverse Plastic Flow Associated With Plastic Indentation

When an indenter is pressed into a surface as in a hardness test, the material beneath the indenter undergoes plastic flow. When the load is removed from the indenter, a second plastic flow occurs in the opposite direction. This paper presents experimental evidence for this reverse plastic flow and mentions a number of practical implications of this behavior.

Mechanisms of plastic deformation of olivine

Olivine deformed experimentally at 5-kb confining pressure undergoes plastic flow by slip on several systems. The active slip system is determined from microscopic study of slip bands, deformation lamellas and kink bands. At temperatures less than 1000°C the slip systems are {110} [001], (100) [001], and (100) [010]. At 1000°C, slip on {0kl} [100], pencil glide in [100], the system shown here to be predominant in naturally deformed terrestrial olivine, occurs in addition to the system {110} [001] and becomes the predominant mechanism with decreasing strain rate. Dependence of glide mechanism on temperature and strain rate is also observed in diopside. Data of the sort acquired in these experiments may be used to place limits on the possible temperatures and strain rates of naturally deformed rocks.

Instrumentation to control strain rate for materials undergoing plastic flow

An instrument is described which controls the head velocity and, therefore, the strain rate of specimens tested in electromechanical universal testing machines. Within the available speed limits of these machines, a predetermined strain rate is achieved by automatic adjustment of a variable resistance in the speed-control circuit. This adjustment is achieved by coupling a potentiometer to the crosshead movement with a cam. An exact mathematical solution is derived for general cam profiles which give either nondecreasing or nonincreasing strain rates. Numerical results are presented for cams which achieve constant true strain rate in tensile and compression testing. For these cases, instrument calibration curves and tensile stress-strain curves for iron at room temperature are presented.