is the strain free lattice spacing E is the Youngs modulus \u03bd is Poissons

# Is the strain free lattice spacing e is the youngs

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is the strain- free lattice spacing, E is the Young’s modulus, ν is Poisson’s constant and σ φ is the residual stress. For this report, the first part of Equation 4 was used to calculate the strain (Equation 5), where the first measurement for d-spacing in Table 1 was considered as d 0 . ε φψ = d φψ - d 0 d 0 (5) The measurements obtained from the XRD test and calculations for d- spacing and strain are shown in Table 1. Measurement ψ deg sin 2 ( ψ ) Peak pos ( 2 θ ) deg d-spacing (nm) Strain 1 0 0 99.589 0.117119 0 2 26.57 0.2 99.694 0.117029 -0.000845 3 39.23 0.4 99.810 0.116929 -0.001706 4 50.77 0.6 99.934 0.116823 -0.002560 Table 1: Shot-peened steel spring d- spacing and strain results from XRD test. In order to calculate the residual stress, a graph sin 2 ( ψ ) vs ε φψ was plotted (Figure 4), obtaining a linear graph represented by Equation 6. Comparing Equation 4 with Equation 6, it can be deduced that slope -0.0043 is equal to 1+ v E σ φ . Using the properties of the material shown in Table 2 and Equation 7 the residual stress of -694.61 MPa was obtained. Figure 4: Graph sin 2 ( ψ ) vs ε φψ for a shot-peened steel spring. 5
MS43010 - N OVEMBER 25, 2019 y = - 0 . 0043 x + 3 x 10 - 6 (6) Young Modulus (E) MPa Poisson ratio (v) Wavelength ( λ ) nm 210x10 3 0.3 0.178897 Table 2: Shot- peened steel properties. σ φ = - 0 . 0043 E 1 + v = ( - 0 . 0008)(210 x 10 3 ) 1 + 0 . 3 = - 694 . 61 MPa (7) 2. Important is to realize the direction of the stress and if this is compressive or tensile! Draw an arrow in the image below to indicate the direction of the measured stress in this experiment. Explain from the measured peaks why it is compressive or tensile in this direction. Shot peening is a process which affects plastic deformation on the surface, relieves surface tensile stresses and introduces beneficial compressive residual stresses as shown in Figure 5.[ 4 ] The degree and sign of the residual stress depend on degree and nature of the working process, and shot peening is a cold working process where peening is carried out on the surface of a component with small spherical balls called shots.[5] Figure 5: Stress formation during shot peening process[5] XRD is a linear-elastic process which calculates residual stresses in the materials from the strain measured in the crystal lattice. XRD processes do not have significant influence by the hardness of the material, degree of cold work, or preferred orientation.[ 4 ] It is proficient of large spatial resolution, on the order of millimetres and depth resolution on the order of microns. Thus, it can be applied to a wide variety of sample geometries. Through XRD methods, the macroscopic residual stresses and the information associated with the degree of cold working can be achieved simultaneously.[ 4 ] The shallow depth of infiltration of the x-ray beam, on the scale of 8 μ m, is an aid for high-resolution 6
MS43010 - N OVEMBER 25, 2019 subsurface profiles but can be a hindrance when trying to characterize a stress distribution generated by shot peening with just surface measurements.[4] An example of a typical shot-peened surface’s stress depth profile inducing over 400 MPa of compressive residual stress on the subsurface layers of the component is shown in Figure 6. Within the depth, differences in the stress direction and values are confirmed by X-ray diffraction.[5]

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• Spring '18
• Dr. maarten bakker

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