M.G. Stout

Effects of Strain State and Strain Rate on Deformation-Induced Transformation in 304 Stainless Steel: Part I. Magnetic Measurements and Mechanical Behavior

The γ→α transformation in 304 stainless steel can be induced by plastic deformation at room temperature. The kinetics of strain-induced transformations have been modeled recently by Olson and Cohen. We used magnetic techniques to monitor the progress of the γ→α transformation in 304 stainless steel sheet loaded in uniaxial and biaxial tension at both low (10-3 per second) and high (103 per second) strain rates. We found that using the von Mises effective strain criterion gives a reasonable correlation of transformation kinetics under general strain states. The principal effect of increased strain rate was observed at strains greater than 0.25. The temperature increase resulting from adiabatic heating was sufficient to suppress the γ→α transformation substantially at high rates. The consequences of the γ→α transformation on mechanical behavior were noted in uniaxial and biaxial tension. Uniaxial tension tests were conducted at temperatures ranging from 50 to -80°C. We found that both the strain hardening and transformation rates increased with decreasing temperature. However, the martensite transformation saturates at ≈85 pct volume fraction α. This can occur at strains less than 0.3 for conditions where the transformation is rapid. Once saturation occurs, the work hardening rate decreases rapidly and premature local plastic instability results. In biaxial tension, the same tendency toward plastic instability associated with high transformation rates provides a rationale for the low biaxial ductility of 304 stainless steel.

Three-dimensional, finite deformation, viscoplastic constitutive models for polymeric materials

Abstract A general methodology for developing three-dimensional. finite deformation, viscoplastic constitutive models for polymeric materials is presented. The development begins with the presentation of a one-dimensional spring and dashpot construction which exhibits behavior typical of polymeric materials, namely strain-rate dependence, stress relaxation, and creep. The one-dimensional construction serves as a starting point for the development of a three-dimensional, finite deformation, viscoplastic constitutive model which also exhibits typical polymeric behavior. Furthermore, the three-dimensional constitutive model may be easily generalized to incorporate an arbitrary number of inelastic processes, representing (inelastic) microstructural deformation mechanisms operating on different time scales. Strain-rate dependence, stress relaxation, and creep phenomena are discussed in detail for a simple version of the constitutive model. Test data for a particular polymer is used to validate the simple model. It is concluded that the methodology provides a flexible approach to modeling polymeric materials over a wide range of loading conditions.

Consideration of grain-size effect and kinetics in the plastic deformation of metal polycrystals

Abstract This work extends the constitutive model for the prediction of grain-size dependent hardening in f.c.c. polycrystalline metals proposed by Acharya and Beaudoin [1] (Grain-size effect in fcc viscoplastic polycrystals at moderate strains, 1999, in press) to include effects of temperature and strain rate dependence. A comparison is made between model predictions and compression data, taken at varying temperature and strain rate, for pure Ag having two different grain sizes. It is shown that an initial increase in yield stress and concomitant decrease in hardening rate for a fine-grained material, relative to a coarse-grained counterpart, can be captured through initialization of a state variable serving to describe stress response at prescribed reference conditions of temperature and strain rate. A grain-size dependence of hardening rate during parabolic (stage III) hardening is characterized by the evolution of net dislocation density in a finite element model of a polycrystal aggregate. Finally, observations from simulations of deformation of the polycrystal aggregate are introduced into an existing macroscopic constitutive model for metal plasticity based on the mechanical threshold.

Thermally and mechanically induced residual strains in Al-SiC composites

Abstract Neutron diffraction experiments were conducted on 15vol.% whisker and 20vol.% particulate reinforced aluminum/silicon carbide composites subjected to a rapid quench followed by various deformation histories. Corresponding numerical simulations were carried out using an axisymmetric unit cell model, with a phenomenological, isotropic hardening descriotion of matrix plasticity. Thermal expansion and the temperature dependence of material properties were accounted for. For the whisker reinforced matrix, quantitative agreement was generally found between the measured and calculated residual elastic strains. For the particulate reinforced matrix, the calculations tended to overestimate the magnitude of the residual strains parallel to the deformation axis, but very good agreement was obtained transverse to the deformation axis. For the silicon carbide reinforcement, both whisker and particulate, the variation of predicted residual elastic strains along the deformation axis was qualitatively consistent with the measurements, although quantitative agreement was often lacking. Measured and predicted residual strains perpendicular to the deformation axis for the silicon carbide typically were not in agreement. Parametric studies were carried out to ascertain the dependence of calculated flow strengths and residual strains on cell and reinforcement aspect ratio, and on reinforcement spacing and shape.

Mechanical response of zirconium—II. Experimental and finite element analysis of bent beams

Abstract In a companion paper [Acta mater. 2001, 49(15), 3085–3096] we develop a polycrystal constitutive law that incorporates the deformation mechanisms operating in high purity zirconium (Zr) at liquid nitrogen (LN) and room temperature (RT). In this paper we present results of 4-point bending tests performed on beams of highly textured zirconium. These tests have been performed at LN and RT, in two orthogonal bending planes, and up to a strain of approximately 20% in the outermost fibers of the beams. A novel experimental technique, dot-matrix deposition and mapping (DMDM), has been developed and employed to analyze the distribution of local plastic strain and macroscopic deformation in the deformed beams. Automated electron backscatter diffraction (EBSD) pattern analysis has been used to evaluate the textures just below the outermost tensile and compressive surfaces and at the neutral plane. Experimental results compare very well with the predictions of finite element (FE) simulations obtained using the constitutive law developed in Part I. Specifically, we compare local deformation, macroscopic deformation and local texture in the beam. We show that the contribution of twinning to deformation results in different qualitative responses in the compressive and tensile fibers of the bent beam. Our results indicate the necessity of using a constitutive description that accounts for the anisotropy of the aggregate and for its evolution with deformation.

Mechanical properties of bone-shaped-short-fiber reinforced composites

Abstract Short-fiber composites usually have low strength and toughness relative to continuous fiber composites, an intrinsic problem caused by discontinuities at fiber ends and interfacial debonding. In this work a model polyethylene bone-shaped-short (BSS) fiber-reinforced polyester–matrix composite was fabricated to prove that fiber morphology, instead of interfacial strength, solves this problem. Experimental tensile and fracture toughness test results show that BSS fibers can bridge matrix cracks more effectively, and consume many times more energy when pulled out, than conventional straight short (CSS) fibers. This leads to both higher strength and fracture toughness for the BSS-fiber composites. A computational model was developed to simulate crack propagation in both BSS- and CSS-fiber composites, accounting for stress concentrations, interface debonding, and fiber pull-out. Model predictions were validated by experimental results and will be useful in optimizing BSS-fiber morphology and other material system parameters.

Experimental deformation textures of OFE copper and 70:30 brass from wire drawing, compression, and torsion

Inverse pole figures have been made from OFE copper and 70:30 brass samples which were deformed to a von Mises equivalent strain of 1.5 in wiredrawing, compression, and torsion. Measurements were taken from the plane normal to the axis of maximum or minimum principal strain for the cases of tension and compression, respectively. We studied three sections for the specimens deformed in torsion, namely the planes normal to the three cylindrical coordinate axes (Z, R, and π). Our results were consistent with the literature data for both wiredwaring and compression. In wiredrawing we found a duplex fiber texture of [001] and [111] orientations. The amount of the [001] texture was much less for the 70:30 brass. A [011] fiber texture developed in both materials in compression. For the OFE copper, the [011] texture spread toward [113]. In the case of the 70:30 brass there was a spread toward [111]. The inverse pole figures we obtained from the torsion samples had similar trends for both copper and brass. Data from the section taken normal to theR axis showed no distinct preferred orientation. For both materials the Z-section had an increased concentration of [111] poles and a distinct absence of [011] poles. In the case of the copper there was also a slight [001] component. Finally, we found the [011] component in the π-section. This section was also characterized by a lack of [001] or [111] orientations.

A modeling study of the effect of stress state on void linking during ductile fracture

Abstract The deformation and fracture behavior of sheet specimens containing either pairs of “pseudo”-random arrays of equi-sized holes has been examined in both uniaxial and equal-biaxial tension utilizing experiment as well as computer simulation. Our results show for this plane-stress situation that hole linking is always caused by flow localization within the ligaments between neighboring holes. The imposed strains to initiate flow localization and subsequent ligament failure are sensitive to stress state (uniaxial versus biaxial) and the location of the neighboring hole(s). A significant observation is the influence of stress state on the multidirectionality of hole linking paths: specifically, increasing the biaxial component of the stress state increases the number of holes that can participate in a hole-linking process. A related implication is that the strain range over which void linking occurs decreases with increasing triaxiality of the stress state; in effect, after the initiation of void linking, its propagation is accelerated under biaxial or triaxial tension.

Role of geometry in plastic instability and fracture of tubes and sheet

Abstract Conditions for plastic instability and fracture for biaxially loaded tubes are compared to those for a sheet to assess the role of geometry. Thin-walled tubes of 70-30 brass were loaded in combined axial tension-internal pressure. The strains for diffuse instability, local instability and fracture were measured and compared to results on brass sheet. Uniform deformation (up to diffuse instability) was found to be very sensitive to geometry in agreement with theory. The uniform strain in tubes for axial plane strain is twice that for hoop plane strain and the uniform strain in tubes for balanced biaxial tension is only one third of that for sheet. The strain levels for local instability and fracture did not depend on geometry. No significant differences were found for axial vs. hoop loading in tubes and the critical strain levels for tubes were actually somewhat greater than those for sheet. Although the critical local strains are similar, the amount of useful (genera) deformation beyond diffuse instability for tubes is very limited because localization occurs rapidly. In bulged or punched sheet the geometry is stable and localization occurs gradually, providing significant post-uniform deformation.

A composite reinforced with bone-shaped short fibers

Using a model composite system, the authors have demonstrated the concept that bone-shaped short-fiber composites can yield both high strength and toughness, thus avoiding reliance on the interfacial properties as the limiting factor for improving the strength and toughness of short-fiber composites. The higher yield strength and Young`s modulus of bone-shaped short fiber composites demonstrate that bone-shaped short fibers more effectively reinforce the composite matrix, most likely due to more effective cracking bridging and load transfer. The results suggest that an optimized bone morphology, coupled with a weak interface, has the potential to significantly improve both the strength and toughness of short fiber composites. Further study is underway to optimize the fiber morphology to obtain the best combination of strength and toughness.