Calculation Of Resolved Shear Stresses Research Articles

Effect of deformation mode on martensitic transformation in medium Mn steel

In the present work, we have investigated the effect of deformation modes namely uniaxial loading and plane strain loading on martensite transformation in medium Mn TRIP steels, since it plays an important role in influencing formability. Interrupted deformation experiments showed that the martensitic transformation proceeds continuously with plastic strain and is influenced by the specific deformation mode applied. Uniaxially loaded samples underwent a complete austenite to martensite transformation. On the other hand, under plane strain loading, only 70 % of the austenite transformed into martensite, even after fracture had occurred. Through synchrotron and EBSD experiments, we observed that under uniaxial loading, the transformation sequence followed the γ-ε-α′ pathway, whereas, under plane strain, a direct γ-α′ transformation was observed. The intermediate ε-martensite phase is known to facilitate the transformation from austenite to martensite. Consequently, the presence of ε-martensite resulted in a higher degree of austenite transformation in the uniaxial samples. We rationalize the difference in transformation sequences based on resolved shear stress calculations for the two deformation modes.

On the High Formability of AZ31-0.5Ca Magnesium Alloy.

In this work, we investigated the effect of Ca on the formability of the AZ31 Mg alloy. For this purpose, the microstructure, texture, mechanical properties and formability of AZ31 Mg alloy samples containing 0.5 wt. % Ca (AZ31-0.5Ca) were studied. For comparison, the performance of Ca-Free AZ31 alloy samples with similar grain size was also investigated. In addition, formability of this alloy was reached at a high punch speed. The results of this work showed that the addition of 0.5 wt. % Ca can enhance the formability of the AZ31 alloy, which was three times greater than that of the Ca-Free AZ31 alloy. The improved formability was attributed to the formation of (Mg,Al)2Ca particles (~1 μm), which, in turn, contribute to reducing the intensity of the strong basal texture during the primary processing of the alloy. The in-grain misorientation axis analysis determined by electron back-scattered diffraction and critical resolved shear stress calculations carried out by the viscoplastic self-consistent model showed that the non-basal slip systems could be activated in the AZ31-0.5Ca alloy.

An investigation of resolved shear stress on activation of slip systems during ultraprecision rotary cutting of local anisotropic Ti-6Al-4V alloy: Models and experiments

Ti-6Al-4V alloy with local anisotropic characteristics is produced by electropulsing treatment (EPT) and used in ultraprecision rotary diamond cutting to explore the deformation mechanism of the alloy. Two different orientations of lamellar martensite α give rise to the local anisotropic behaviour. Critical resolved shear stress (CRSS) is introduced in this paper to investigate the slip modes of the hexagonal closest packing martensite. A geometrical and physical model is also proposed for calculation of resolved shear stresses on various slipping systems. The results show that glide occurs in some certain directions on the condition that resolved shear stress equals or exceeds the CRSS. The cutting force varies with martensitic orientations, which is supposedly due to the combined effects of lamellar α phase sizes and the coordination or competition of diverse slipping directions.

Time-resolved light emission of a, c, and r-cut sapphires shock-compressed to 65 GPa

To investigate light emission and dynamic deformation behaviors, sapphire (single crystal Al2O3) samples with three crystallographic orientations (a, c, and r-cut) were shock-compressed by the planar impact method, with final stress ranges from 47 to 65 GPa. Emission radiance and velocity versus time profiles were simultaneously measured with a fast pyrometer and a Doppler pin system in each experiment. Wave profile results show anisotropic elastic-plastic transitions, which confirm the literature observations. Under final shock stress of about 52 GPa, lower emission intensity is observed in the r-cut sample, in agreement with the previous report in the literature. When final shock stress increases to 57 GPa and 65 GPa, spectral radiance histories of the r-cut show two stages of distinct features. In the first stage, the emission intensity of r-cut is lower than those of the other two, which agrees with the previous report in the literature. In the second stage, spectral radiance of r-cut increases with time at much higher rate and it finally peaks over those of the a and c-cut. These observations (conversion of intensified emission in the r-cut) may indicate activation of a second slip system and formation of shear bands which are discussed with the resolved shear stress calculations for the slip systems in each of the three cuts under shock compression.

Plastic deformation of a porous bcc metal containing nanometer sized voids

Nanoporous materials, can present an outstanding range of mechanical properties. Both molecular dynamics and dislocation analysis were used to evaluate and quantify the evolution of plasticity in a porous Ta single crystal containing randomly placed voids with 3.3nm radii and average initial porosity of 4.1%, when subjected to uniaxial compressive strain. Nanovoids act as effective sources for dislocation emission. Dislocation shear loops nucleate at the surface of the voids and expand by the advance of the edge component. The evolution of dislocation configuration and densities were predicted by the molecular dynamics calculations and successfully compared to an analysis based on Ashby’s concept of geometrically-necessary dislocations. Resolved shear stress calculations were performed for all bcc slip systems and used to identify the operating Burgers vectors in the dislocation loops. The temperature excursion during plastic deformation was used to estimate the mobile dislocation density which is found to be less than 10% of the total dislocation density.

Shock response of single crystal and nanocrystalline pentaerythritol tetranitrate: Implications to hotspot formation in energetic materials

We investigate shock response of single crystal and nanocrystalline pentaerythritol tetranitrate (PETN) with a coarse-grained model and molecular dynamics simulations, as regards mechanical hotspot formation in the absence or presence of grain boundaries (GBs). Single crystals with different orientations, and columnar nanocrystalline PETN with regular hexagonal, irregular hexagonal, and random GB patterns, are subjected to shock loading at different shock strengths. In single crystals, shock-induced plasticity is consistent with resolved shear stress calculations and the steric hindrance model, and this deformation leads to local heating. For regular-shaped hexagonal columnar nanocrystalline PETN, different misorientation angles lead to activation of different/same slip systems, different deformation in individual grains and as a whole, different GB friction, different temperature distributions, and then, different hotspot characteristics. Compared to their regular-shaped hexagonal counterpart, nanocrystalline PETN with irregular hexagonal GB pattern and that with random GBs, show deformation and hotspot features specific to their GBs. Driven by stress concentration, hotspot formation is directly related to GB friction and GB-initiated crystal plasticity, and the exact deformation is dictated by grain orientations and resolved shear stresses. GB friction alone can induce hotspots, but the hotspot temperature can be enhanced if it is coupled with GB-initiated crystal plasticity, and the slip of GB atoms has components out of the GB plane. The magnitude of shearing can correlate well with temperature, but the slip direction of GB atoms relative to GBs may play a critical role. Wave propagation through varying microstructure may also induce differences in stress states (e.g., stress concentrations) and loading rates, and thus, local temperature rise. GB-related friction and plasticity induce local heating or mechanical hotspots, which could be precursors to chemical hotspot formation related to initiation in energetic materials, in the absence of other, likely more effective, means for hotspot formation such as void collapse.

Characterization of deformation anisotropies in an α-Ti alloy by nanoindentation and electron microscopy

The crystallographic dependence of the mechanical responses of an α-Ti–7wt.% Al alloy was measured by nanoindentation using spherical and Berkovich indenters. Both elastic moduli and hardness responses of indents on the (0001), (1¯100) and (1¯21¯0) planes were quantified. The dislocation structures resulting from indentation were characterized by electron microscopy. While scanning electron microscopy techniques were used for the observation of surface slip structures, site-specific focused-ion-beam thin foil preparation and scanning transmission electron microscopy techniques were employed for the imaging of sub-surface dislocation structures. Elastic modulus, hardness and load at pop-in were found to vary with crystallographic orientation. Indentation-induced plasticity was found to occur by multiple slip/twin mechanisms and to be dependent on crystal orientation, although 〈a〉 slip on (0001) planes was found to be common to all orientations. The observed dislocation structures are rationalized on the basis of theoretical predictions based on the anisotropic elastic contact analysis and resolved shear stress calculations.

On the crystallographic anisotropy of nanoindentation in pseudoelastic NiTi

We use a nanoindenter with a Berkovich tip to study local mechanical properties of two polycrystalline intermetallics with a B2 crystal structure, NiAl and NiTi. We use orientation imaging scanning electron microscopy to select a relevant number of grains with appropriate sizes and surface normals parallel to 〈001〉, 〈101〉 and 〈111〉. As a striking new result, we find a strong crystallographic orientation dependence for NiTi. This anisotropy is less pronounced in the case of NiAl. For NiTi, the indentation force required to impose a specific indentation depth is highest for indentation experiments performed in the 〈001〉 direction and lowest along the 〈111〉 direction. We consider transmission electron microscopy results from cross-sections below the indents and use molecular dynamics simulations and resolved shear stress calculations to discuss how this difference can be accounted for in terms of elementary deformation and transformation processes, related to dislocation plasticity (NiAl and NiTi), and in terms of the stress-induced formation and growth of martensite (NiTi). Our results show that the crystallographic anisotropy during nanoindentation of NiTi is governed by the orientation dependence of the martensitic transformation; dislocation plasticity appears to be less important.

Fatigue Crack Growth Behavior of PWA 1484 Single Crystal Superalloy at Elevated Temperatures

A study was done to determine the fatigue crack growth behavior of a PWA 1484 single-crystal nickel-base superalloy in a temperature range of 427°C to 871°C. Two distinctive failure modes were observed, which were a function of both temperature and frequency. At lower temperatures and higher frequencies crack growth occurred on the {111} octahedral slip planes at an oblique angle to the loading direction. Higher temperatures and decrease in frequencies favored angle to the loading direction. Higher temperatures and decrease in frequencies favored a Mode I type failure process. The failure mode transitions were explained by invoking arguments based on environmental damage mechanisms. The fatigue crack growth rate data were analyzed using three different crack driving force parameters. The parameters investigated consisted of the Mode I stress intensity parameter corrected for the inclined crack trajectory, and two different octahedral Mode II parameters, which are based on the calculation of resolved shear stresses on the {111} slip systems. The Mode I ΔK parameter did a fair job in correlating the data but did not collapse it into a single narrow band. The two octahedral crack driving force parameters, ΔKRSS and a newly proposed ΔKOCT, collapsed all the data into a single narrow band. In addition to correlating the fatigue crack growth rates, the two octahedral parameters also predicted the {111} planes on which the crack growth took place.

The movement of slip dislocations in internally twinned martensite

A model for the passage of a/2 〈111〉 slip dislocations through a body centered cubic martensite plate internally twinned on {112} has been evaluated quantitatively from a computer calculation of resolved shear stresses for the various operative slip systems. The results are restricted to slip on {110} planes and show that whenever the slip dislocation has to assume a “zig-zag” configuration due to the presence of the internal twins the most favourable conditions occur when the two dislocation components share the same slip plane. The results of the calculation predict that internally twinned martensite should be stronger than untwinned lath martensite by a factor in the region of 1.05 to 1.20. This is in reasonable agreement with quoted experimental values of between 1.08 and 1.30.