The Effect of Residual Stresses on Stress–Strain Curves Obtained via Profilometry‐Based Inverse Finite Element Method Indentation Plastometry

Abstract

This paper concerns, the effect of (unknown) residual stresses in the near‐surface region of a sample on outcomes of an indentation plastometry technique for obtaining stress–strain relationships, using relatively large spherical indenters. The technique is based on the iterative finite element method (FEM) simulation of indentation, so as to infer the true stress–strain curve of the material (with the target outcome being the profile of the residual indent). It is expected that residual stress levels (if significant compared with the yield stress) are likely to influence the outcome, and indeed this forms the basis of many attempts to measure residual stresses in this way (using a known stress–strain curve). However, there are important issues of sensitivity here, which affect the reliability of such procedures and are also relevant to the accuracy of stress–strain curves inferred from measurements made on samples containing unknown levels of residual stress. Herein, both experimental work on samples with (equal‐biaxial) residual stresses created by the application of external loads and extensive FEM modeling to explore various scenarios are covered. The main conclusion is that the sensitivities involved are in general very low, particularly with relatively deep indentation. Inferred stress–strain curves are thus likely to be quite accurate, even in the presence of relatively high levels of residual stress. Conversely, the measurement of residual stress levels via this procedure is likely to be rather inaccurate, although the reliability is improved using shallow penetration (low ratio of depth‐to‐indenter radius). It is also noted that tensile residual stresses tend to influence outcomes more strongly than compressive ones.

Profilometry‐Based Inverse Finite Element Method Indentation Plastometry

“…The most relevant work in this area [ 70–75 ] has involved experimental indentation of samples in which controlled “artificial” residual stresses were created by the external application of (equal or unequal biaxial) forces. Most of these studies have been based on the load–displacement plot being used as the experimental outcome, although in some of them [ 71,73 ] the residual indents were also viewed optically, with it being noted that their shapes became (approximately) elliptical when the residual stresses were unequal.…”

“…Most of these studies have been based on the load–displacement plot being used as the experimental outcome, although in some of them [ 71,73 ] the residual indents were also viewed optically, with it being noted that their shapes became (approximately) elliptical when the residual stresses were unequal. However, the recent study of Burley et al [ 75 ] was based on PIP methodology, giving scope for quantification, as well as detection, of anisotropic residual stresses (in a similar way to that described in Section 3.2 for anisotropy in the plasticity of the sample).…”

Indentation Plastometry of Very Hard Metals

“…[ 9 ] It has already been applied to a thin plasma‐sprayed layer [ 10 ] and (anisotropic) additively manufactured material, [ 11 ] both Ni‐based superalloys. It has also been confirmed [ 12 ] that residual stresses are unlikely to affect the reliability of extracted stress–strain curves. Important points concerning optimization include the major advantages of a spherical indenter [ 5 ] and the requirement to deform a volume large enough for its mechanical response to be representative of the bulk—usually requiring it to be a “many‐grained” assembly.…”

Formation of Residual Stresses during Discontinuous Friction Treatment

“…They are among the most critical indicators of the parts' surface layers quality. Thus, the residual compressive stresses in the machine parts' surface layers increase their resistance to fatigue failure, and the tensile, on the contrarydecreases [13,14]. Knowing the patterns of the 1st kind residual stresses formation can predict and The formation of the someone or other residual stresses plot in the surface layers of the metal depends on the processing conditions, the applied technological medium, the physical and mechanical properties of the processed material.…”