Surface residual stresses induced by torsional plastic pre-setting of solid spring bar
Introduction
Residual stresses in mechanical components are a result of technological processes. Residual stresses usually arise due to additional deformation during cold surface deformation such as cold drawing, stamping, shoot peening, cold rolling, and/or pre-setting. Residual stresses play a significant role in stress magnitude and the failure of a component. One example of residual stresses preventing failure is the cold rolling of the surface of mechanical component in order to induce surface compressive stresses that improve the fatigue life of the component. Torsion specimens were surface cold-rolled and plastic pre-strained in the torsion direction. Surface rolling increases the compressive stress in the surface layers of the specimen, whilst the pre-setting acts in-depth. Both tensile and compressive stresses are in equilibrium within the material. During the usage of the mechanical part residual stresses are cumulative with applied ones. If the latter are time changing, and if the mechanical component is loaded with fatigue, then residual stresses can significantly affect crack initiation. Maximum applied stresses are mostly on the surface of mechanical parts (bending, torsion, or a combination), and the geometric changes and rough surface contribute an additional stress concentration. When the tensile residual stresses cumulate with the tensile applied stress on the surface of the mechanical component, it leads to a very unfavourable situation. Compressive residual stress on the surface is much more desirable and is subtracted from the applied tensile stress during use of the mechanical part. With the use of appropriate manufacturing processes (for example cold surface rolling, or pre-setting into the plastic range) it is possible to add compressive residual stress on the surface of the mechanical component.
The authors in [1] have investigated the influence of residual stresses due to pre-setting on the lifetime of the torsion specimens from spring steel. It was proposed that with an increased pre-setting angle, the lifetime falls at the same amplitude of the applied stress ratio (minimum stress/maximum stress) R=0 torsional fatigue. The analytical procedure for determining residual stresses based on the experimentally determined τ–γ characteristics was discussed.
In Ref. [2] authors investigated the influence of residual compressive stress on the lifetime of a torsion alternately-loaded hollow specimen made of spring steel. Residual compressive stress was simulated by a constant axial compressive force, and the specimen was loaded by alternating torsional fatigue at the same time. It has been established that the lifetime of the specimen with the increasing of the compressed axial pre-loading at alternating torsional fatigue, increases as well up to a certain point.
The authors in [3] studied crack shapes and their growth rate for S45 steel specimens under various combinations of torsion and constant axial force loads. They state that the crack propagation angle is about 45° for various loading amplitudes, that the static tension axial force together with cyclic torsion causes the accelerated growth of a crack and lowers the service life, and that the compression axial force, together with torsion, considerably increases the service life and does not affect the crack propagation angle. It was also stated that the direction of crack propagation depends on alternating stress and does not depend on median stress; however, the service life does depend on the latter.
The authors in [4] developed a method for investigating the growth of micro-structural short cracks in a ductile crystalline material. The crack itself was modelled by a distribution of dislocation dipoles of finite length, whilst the local plasticity was developed by the emission and annihilation of discrete dislocations. Investigations of a short-edged crack showed that the competition between increasing global stress due to crack advance and the increasing shielding effect on the crack׳s tip from dislocations within the plastic zone influences the crack growth. The distance between the crack tip and the grain boundary is shown to influence the crack growth characteristics, whilst the spreading of plasticity through a grain boundary was found to somewhat retard the crack growth. The theoretical consideration of the fatigue process explained how it is possible to extend the lifetimes of mechanical parts loaded with cyclical torsion fatigue, by using compressed pre-stress in the axial direction [5]. A method of discrete dislocations was introduced in order to explain the process within the crystalline material lattice. This process can lead to increase in the lifetimes of compressed pre-stressed mechanical parts subjected to alternate torsion fatigue-loading.
Other investigations have been performed in the past for smooth and pre-cracked specimens subjected to combined torsion and axial loadings [7], [8]. These results confirm that high-cycle fatigue is a stress controlled process. Unfortunately, not many investigations have been concerned with low-cycle multi-axial fatigue. Investigations of the multi-axial fatigue of a specimen with a surface defect show that their results agree with the most popular multi-axial fatigue criteria that of a critical plane criterion [6], [7], [9]. The problem of residual stresses was extensively studied in several articles [10], [11], [12], [13], [14]. Especially, the combined loads are relevant for the problem under investigation. This problem was studied by Zyczkowski [15] and Kobelev [16], [17]. Kobelev study an elastic-plastic work-hardening deformation under combined bending and torsion and residual stresses in helical springs. He fund that theory of residual stresses in helical springs allows calculating the stresses during the coiling and presetting.
Residual stresses were introduced into the surface of the torsion test specimen by means of surface cold rolling and using a torsional pre-setting.
The article discusses residual stress distribution on the surface of the torsion loaded specimen during the process of pre-setting and a comparison with analytical and numerical calculation as well.
Section snippets
Material characteristics and specimens
Torsion and tensile specimens were made from high-strength spring fine-grain steel grade VCN. The chemical composition is listed in Table 1 as weight%. The used material was hot rolled, forged, and soft annealed during the manufacturing process. The final shape and specimen properties were achieved by the following mechanical processes: programmed turning, milling, polishing and at torsion specimens cold rolling of their surface to a roughness of Ra≤0.1 μm. The geometry of a specimen is shown in
Determination of the residual stresses using the calculation procedure
A characteristic τ–γ was established on the basis of T–Θ measurement, Fig. 4. From the theory of the elasticity, the relation between the twist angle Θ and the shear strain γ is known, which applies to both linear and non-linear part of the characteristics, Fig. 5andwhere is α=Θ/l, a reduced angle of the cross-section per unit length of the specimen.
The relationship between torsional shear stress τ and torque T in the range of elastic-plastic deformation can be written as
Determination of the residual stress in a pre-strained torsion specimen by means of FEM methods
ABAQUS software No-6.11, was used, the numerical model has been generated using the 378,480 finite elements with 8 nodes “CONTINUUM 3D”. Fig. 8 shows the numerical model and residual stress distribution τyz through the cylindrical specimen after torsional unloading at maximum pre-setting shear strain of γps=0.043. Fig. 9, Fig. 10 show the stress distribution throughout the specimens׳ cross-section.
Two types of nonlinearities in the FEM analysis were taken into account. Material nonlinearity,
Measurement of residual stresses with the x-ray diffraction method
X-ray diffraction can be used to measure residual stress using the distances between crystallographic planes, i.e., d-spacing, as a strain gauge. When the material is in tension, the d-spacing increases and, when under compression, the d-spacing decreases [19]. Stress can be determined from the measured d-spacing. X-rays diffract from crystalline materials at known angles 2θ according to Bragg׳s law: nλ=2d sin θ, and ε=Δd/d=−Δθ cot θ, where n is order of diffraction, λ is the wavelength of the
The results of measurements of the residual stresses
Residual stresses were measured on the surface of the specimen during the torsion pre-setting. The specimen was clamped in the device for torsional loading, shown in Fig. 12. The principal stresses, which in the pure torsion operate at an angle of 45° with respect to the direction of shear stress, were measured; namely in the directions of +45° and −45°, Fig. 13. Fig. 14 shows a distribution of the residual stresses on the surface of the specimen during the pre-setting in both principal
Conclusions
- a)
Residual stresses on the surface of a round specimen during torsional pre-setting in the principal directions of +45° and of −45°, were measured, Fig. 14. The compress principal stress component, measured in the direction of +45°, is represented by the curve 1a–2a–3a in Fig. 14, while, the tensile one, measured in the direction of −45°, is represented by the curve 1–2–3. The distributions of both stress components are linear, as long as the material is in elastic state, and are non-linear, when
Acknowledgements
The authors would like to thank for the measurement of Mr. Janne Suoknuuti of the Stresstech Oy, Finland and Mr. Jiri Malec of PCS s.r.o Zdar nad Sazavou, Czech Republic. The financial support of the Slovenian Research Agency-ARRS under Program P2-0137 is gratefully acknowledged.
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