Experimental and theoretical studies of the superposition of intergranular and macroscopic strains in Ni-based industria
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I.
INTRODUCTION
RESIDUAL stresses in an engineering component are the stresses existing within the component when it is not subjected to external loads. These are generated by thermomechanical processing during manufacture. The residual stresses are equilibrated over the sample but they are necessarily nonuniformly distributed throughout. Diffraction methods have been used for 70 years[1] to assess these stresses by measuring elastic residual strains, yet there are a number of problems with the interpretation of residual strains in terms of residual stresses that are unresolved. An excellent and thorough review of the field was provided by Noyan and Cohen[2] 10 years ago. Residual stresses are very often the result of inhomogeneous deformation of the component so that some parts of it have deformed elastically while other parts have deformed plastically. The case[3] of the residual stress generated in a plate subjected to a bending moment, so that the region close to the neutral axis deforms elastically whereas the region near the surface is plastically deformed, illustrates this point. However, inhomogeneous deformation happens on three length scales in polycrystalline materials; the scale of the sample size (usually .1 mm), the scale of the grain size (1 mm to 1 mm), and the scale of crystal defects (,,1 mm). The first gives rise to the macroscopic stress field, often referred to as the type-1 stress, illustrated by the case of the bent plate.[3] The inhomogeneity on the scale of the grain size occurs because of the anisotropy of slip in the different crystallographic directions and because of elastic anisotropy at the crystalline level. Different crystallographic orientations of grains deform differently, both elastically and plastically, when subjected to stresses exceeding the yield point. The elastic strains in the different T.M. HOLDEN, Principal Research Officer, is with the Neutron Program for Materials Research, National Research Council of Canada, Chalk River Laboratories, Chalk River, ON, Canada K0J 1J0. C.N. TOME´, Member of the Technical Staff, is with the Materials Science and Technology Division, Los Alamos National Laboratory, Los Alamos, NM 87545. R.A. HOLT, Director, is with the Fuel Channels Division, AECL, Chalk River Laboratories, Chalk River, ON, Canada K0J 1J0. Manuscript submitted November 13, 1997. METALLURGICAL AND MATERIALS TRANSACTIONS A
crystallographic orientations of grains resulting from this process are termed intergranular strains and are often referred to as type-2 strains. The third type of stress is generated by the dislocations and defects within the grains and is not treated in this article. A general source of problems arising in the interpretation of strain in terms of stress is that diffraction measures the combination of the strain corresponding to the macroscopic stress field as well as the intergranular strain characteristic of the particular reflection (hkl ) used to make the observations. In the X-ray diffraction method, measurements are usually made of the lattice
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