Effect of the grain size on the wavelength of localized strain in aluminum specimens in tension

This paper studies the dependence of the wavelength of localized plastic strain at the parabolic stage of strain hardening on the grain size in polycrystal aluminum. This dependence is determined in the grainsize range 10^–2 – 10 mm. The effect of the grain size on the character of the plasticflow curve is studied.     

New Theory of Flight

We present a new mathematical theory explaining the fluid mechanics of subsonic flight, which is fundamentally different from the existing boundary layer-circulation theory by Prandtl–Kutta–Zhukovsky formed 100 year ago. The new theory is based on our new resolution of d’Alembert’s paradox showing that slightly viscous bluff body flow can be viewed as zero-drag/lift potential flow modified by 3d rotational slip separation arising from a specific separation instability of potential flow, into turbulent flow with nonzero drag/lift. For a wing this separation mechanism maintains the large lift of potential flow generated at the leading edge at the price of small drag, resulting in a lift to drag quotient of size 15–20 for a small propeller plane at cruising speed with Reynolds number \({Re\approx 10^{7}}\) and a jumbojet at take-off and landing with \({Re\approx 10^{8}}\) , which allows flight at affordable power. The new mathematical theory is supported by computed turbulent solutions of the Navier–Stokes equations with a slip boundary condition as a model of observed small skin friction of a turbulent boundary layer always arising for \({Re > 10^{6}}\) , in close accordance with experimental observations over the entire range of angle of attacks including stall using a few millions of mesh points for a full wing-body configuration.     

Experimental Study on Three-Dimensional Deformation Field of Portevin–Le Chatelier Effect Using Digital Image Correlation

In view of its high precision and high efficiency, three-dimensional digital image correlation (3D-DIC) is widely used to accurately measure full-field deformation. A spatiotemporal experimental study using 3D-DIC to explore the Portevin–Le Chatelier (PLC) deformational behavior, provides a new insight into the whole 3D deformation field, including the out-of-plane displacement, and in particular the relationship between the serrations and the strain field in the deformation bands corresponding to individual serrations. Specimens 1, 2 and 3 mm thick of 5456 Al-based alloy were tested in uniaxial tension at room temperature at strain rates from 1.8 × 10^?4 to 9.1 × 10^?3s^?1. The spatial and temporal characteristics of the strain localization were quantitatively analyzed. The out-of-plane displacement increment field (w) of the localized bands was observed by 3D-DIC, and found to be related to the specimen thickness and the in-plane strain increment. The largest displacement increments were respectively 15, 10 and 5 μm for 3, 2 and 1 mm specimens at maximum strain increment of about 12000 με. The elastic shrinkage outside the deformation bands was found to be an essential characteristic of the PLC effect. The width of the PLC band (w_band) increased with increasing thickness; the angle of the PLC band (??_band) was not affected by either specimen thickness or serration amplitude. Temporally, the serrations in the plots both of in-plane strain and out-of-plane displacement vs. time coincided throughout the entire loading procedure. When PLC banding occurred, the serration amplitude within the bands was found to be proportional to the maximum strain increment in the direction of the applied tensile force (??_max).     

Dynamic strain aging and related instabilities: experimental,theoretical and numerical aspects

Experimental data from uniaxial tensile tests on smooth and notched specimens of aluminium alloy 5083-H116 show that the material exhibits negative strain-rate sensitivity for strain rates within a certain range. The negative strain-rate dependence, which is attributed to dynamic strain aging, leads to serrated stress–strain curves, discontinuous plastic flow and propagating deformation bands during plastic straining (also denoted as the Portevin–Le Chatelier effect). Band analysis and linear perturbation analysis are performed using simple elastic-viscoplastic constitutive equations that include negative strain-rate sensitivity in a simplified manner. The negative strain-rate sensitivity allows for jumps in the plastic strain rate, which in turn permits the existence of localisation bands for the elastic-viscoplastic model. The simple elastic-viscoplastic constitutive model has been implemented in LS-DYNA, and non-linear finite element simulations of smooth and notched tensile test specimens are performed, allowing more detailed investigations into the effects of the negative strain-rate sensitivity on the material's behaviour.     

Influence of Portevin-Le Chatelier Effect on Shear Strain Path Reversal in an Al-Mg Alloy at Room and High Temperatures

The main objective of this study is to characterize the mechanical behaviour of an Al-Mg alloy in conditions close to those encountered during sheet forming processes, i.e. with strain path changes and at strain rates and temperatures in the range 1.2×10^?3–1.2×10^?1 s^?1 and 25–200°C, respectively. The onset of jerky flow and the interaction of dynamic strain ageing with the work-hardening are investigated during reversed-loading in specific simple shear tests, which consist of loading up to various shear strain values followed by reloading in the opposite direction, combined with direct observations of the sample surface using a digital image correlation technique. Both strain path changes and temperature are clearly shown to influence the occurrence and onset of the Portevin-Le Chatelier (PLC) effect. Moreover, the Bauschinger effect observed in the material response shows that the PLC effect has a major influence on the kinematic contribution to work-hardening as well as its stagnation during the reloading stage, which could open up interesting lines of research to improve theoretical plasticity models for this family of aluminium alloys.     

A Combined Theoretical/Experimental Approach for Reducing Ringing Artifacts in Low Dynamic Testing with Servo-hydraulic Load Frames

One of the most challenging tasks facing computer-aided engineering (CAE) analysis is the acquisition of accurate tensile test data that spans quasi-static to low dynamic (10^?5/s?≤ $ \overset{.}{\varepsilon } $ ≤5?×?10²/s) strain rates ( $ \overset{.}{\varepsilon } $ ). Critical to the accuracy of data acquired over the low dynamic range is the reduction of ringing artifacts in flow data. Ringing artifacts, which are a consequence of the inertial response of the load frame, are spurious oscillations that can obscure the desired material response (i.e. load vs. time or load vs. displacement) from which flow data are derived. These oscillations tend to grow with increasing strain rate and peak at the high end of the low dynamic range on servo-hydraulic tensile test frames. Common practices for addressing ringing are data filtering, which is often problematic since filtering introduces distortion in smoothed material data, or trial-and-error design of test specimen geometries. This renders techniques for reducing ringing based upon the mechanics of the load frame and optimization of tensile specimen geometry quite attractive. In the present paper, relationships between load, stress wave propagation, and specimen geometries are addressed, to both quantify ringing and to develop specimen designs that will reduce ringing. A combined theoretical/experimental approach for tensile specimen design was developed for reducing ringing in flow data over the low dynamic range of strain rates (10^?5/s≤ $ \overset{.}{\varepsilon } $ ≤5?×?10²/s). The single camera digital image correlation (DIC) method was used to measure the displacement fields and strain rates with specimens resulting from the combined theoretical/experimental approach. While the approach was developed on a specific commercial load frame with a TRIP steel subject to a two-step quenching and partitioning heat treatment (Q&P980), it is readily adaptable to other servo-hydraulic load frames and metallic alloys. The developed approach results in a 90 % reduction in ringing artifact (with no filtering) in a tensile flow curve for Q&P980 at $ \overset{.}{\varepsilon}\kern-4pt $ = 5?×?10²/s. Results from split Hopkinson bar tests of Q&P980 were performed at $ \overset{.}{\varepsilon } $ = 500/s and compare favorably with the test data generated by the developed testing approach. Since the Q&P980 steel represents a new generation of advanced high strength steels, we also evaluated its strain rate sensitivity over the low dynamic range.     

The effect of inhomogeneous plastic deformation on the ductility and fracture behavior of age hardenable aluminum alloys

The role of alloy composition, grain structure, precipitate microstructure, and precipitate dislocation interactions on the plastic deformation characteristics and the resulting fracture behavior of two isotropic Al–Li–Cu–X alloys designated AF/C-458 (1.8 w/o Li) and AF/C-489 (2.1 w/o Li) was examined. Inhomogeneous deformation due to strain localization from the shearing of the δ′ (Al₃Li), θ′ (Al₂Cu), and T₁ (Al₂CuLi) precipitates lead to fine and coarse planar slip for the AF/C-458 and AF/C-489 alloys, respectively. The intensity of this planar slip was predicted through slip intensity calculations using precipitate density measurements, dislocation particle interactions, and grain boundary misorientation-slip continuity statistics. The slip intensity predictions were corroborated through atomic force microscopy (AFM) measured slip height offsets on the polished surface of single aged and 2% plastically strained tensile samples. Our results suggest that the low ductility of AF/C-489 in comparison to AF/C-458 is primarily due to the much larger slip lengths, i.e. grain size, which increased the strain localization and stress concentrations on grain boundaries, thus promoting low-energy intergranular fracture.     

Wall slip and multi-tier yielding in capillary suspensions

Impact of wall slip on the yield stress measurement is examined for capillary suspensions consisting of cocoa powder as the dispersed phase, vegetable oil as the continuous primary fluid, and water as the secondary fluid using smooth and serrated parallel plates. Using dynamic oscillatory measurements, we investigated the yielding behavior of this ternary solid-fluid-fluid system with varying particle volume fraction, ?, from 0.45 to 0.65 and varying water volume fraction, ?_w, from 0.02 to 0.08. Yield stress is defined as the maximum in the elastic stress (G^′γ), which is obtained by plotting the product of elastic modulus (G^′) and strain amplitude (γ) as a function of applied strain amplitude. With serrated plates, which offer minimal slippage, capillary suspensions with ? ≥?0.45 and a fixed ?_w =?0.06 showed a two-step yielding behavior as indicated by two peaks in the plots of elastic stress as a function of strain amplitude. On the other hand with smooth plates, the capillary suspensions showed strong evidence of wall slip as evident by the presence of three distinct peaks and lowered first yield stresses for all ? and ?_w. These results can be interpreted based on the fact that a particle-depleted layer, which is known to be responsible for slip, is present in the vicinity of the smooth surfaces. The slip layer presents itself as an additional “pseudo-microstructure” (characteristic length scale) besides the two microstructures, aqueous bridges and solid particle agglomerates, that may occur in the system. With serrated plates, both the yield stresses (σ₁σ₂) and storage moduli plateau at lower strain (before the first yield point) and at higher strain (before the second yield point) (G\(^{\prime }_{p1}\), G\(^{\prime }_{p2}\)) were found to increase with ? (at a fixed ?_w =?0.06) following power-law dependences. Similarly with increasing ?_w (0.02 – 0.08) at a fixed ? =?0.62, the system behaved as a solid-like material in a jammed state with particles strongly held together as manifested by rapidly increasing σ₁ and σ₂. The usage of smooth surfaces primarily affected σ₁ which was reflected by an approximately 70–90% decrement in the measured σ₁ for all values of ?. By contrast, σ₂ and G\(^{\prime }_{p2}\) were found to be unaffected as shown by close agreement of values obtained using serrated geometry due to vanishing slip layers at higher strain amplitudes.