Yield stress increase in a W/Cu composite observed by neutron diffraction

Abstract

Ceramic matrix composites with a ductile reinforcement phase can be produced by infiltrating a metal melt into a porous ceramic preform [1, 2]. Due to the thermal expansion mismatch, residual stresses of opposite signs develop in the ceramic and metal phase. For alumina/aluminum composites, the tensile stresses of the metal phase can exceed several times its bulk yield stress [3, 4]. This phenomenon may be called “yield stress increase” and was first observed in mechanically constrained metal wires by Ashby et al. [5]. The magnitude of the yield strength increase depends on the diameter of the ductile ligaments, their shape and connectivity [3]. In this study, exceptionally high residual stresses have been observed in the copper phase of a tungsten/copper composite with a graded interpenetrating network microstructure. These stresses are about 16 times larger than the yield stress of bulk, age-hardened copper. The graded W/Cu composite was produced from tungsten powder containing 2 wt % Ni. From this powder, a body of 57% relative density and an average grain size of 14 μm was produced by partial sintering. The porosity was locally increased by anodic oxidation in 2 M NaOH at 8.5 mA cm−2 for 165 h [6]. The resulting tungsten preform with a graded porosity was infiltrated with molten electrolyte copper at 1250 ◦C in a hydrogen atmosphere for 1/2 h. After cooling to room temperature, a composite with a gradient in the copper content along one direction (called depth) was obtained (see Fig. 1). The composite was dense. Determination of Young’s modulus of the composites and phase contrast acoustic microscopy both indicate that no microcracks were present at the tungsten/copper interfaces. Image analysis of optical micrographs showed a gradient in copper content from 49 to 66 vol % (Fig. 2). The electrochemical process also introduces a gradient in the specific interface area into the composite.1 The specific interface area is a measure of the thickness of the average copper ligaments and hence the mechanical constraint exerted on the copper phase. The copper-rich region of the graded composite had a specific interface area of 0.13 μm−1 whereas the region of low copper content had a specific interface area of 0.33 μm−1. Assuming cylindrical copper ligaments of uniform diameter, one calculates copper ligament diameters between 30 and 12 μm. Neutron diffraction allows one to determine the stress tensor in the tungsten and copper phase σ = σ (z) as a function of depth z by selecting the probe volume using appropriate beam collimators. The present measurements were done using the D1A diffractometer at the Institute Laue-Langevin (ILL), Grenoble. D1A is equipped with a long scattered beam collimator resulting in a probe volume of ≈1 mm3 [7]. The measured strain 2= 2(h k l, φ, ω, z) depends on the measurement direction (φ, ω) with respect to the sample coordinate system. Furthermore, 2 depends on z because of the copper concentration gradient. Copper is an elastically anisotropic material, therefore 2= 2(h k l, φ, ω, z) also depends on the lattice plane indices (h k l). To account for the anisotropy, we measured the Cu(1 1 1)and the Cu(3 1 1)-reflection of copper. The diffraction experiments on three samples showed that the copper phase is textured and can be regarded as one single crystal. This texture results from the solidification process, when the solidification front takes on one single crystallographic orientation. Because of the texture, we had to search for suitable sets of tilting angles (φ, ω) to record measurable intensities [8]. Because tungsten is elastically isotropic, we worked with the W(1 1 1)-reflection only. From the measured 2(h k l, φ, ω), the stress tensor σ (z) was calculated at all selected z-values according to Hooke’s law [9]. Single-crystal elastic compliances were used, because the probed volume consisted essentially of a single crystal.2 Fig. 3 shows for both phases the three components σ11, σ22 and σ33 of σ (z) expressed in the principal axes system. For copper, the stress is relaxed at the surface where the copper concentration is highest. At great depths (z<−3 mm), where the copper concentration goes to zero, tensile stress exists, and in the intermediate region compressive stress is present. The tungsten phase has stresses with opposite depth dependence. At the free surface, where the tungsten concentration was low, tensile stress is found. In the intermediate region, tensile stress still exists, which drops to zero at great depths, where the tungsten concentration rises to 100%. This observed depth dependence can be qualitatively explained by the mechanical equilibrium conditions and the lever rule for stresses in a two-phase material.3 At any depth z, the concentration-weighted stresses in both phases balance each other (as long as no interface failure occurs). Stresses at different depths z