0 2 4 6 8 10 0 200 400 600 800 1000 1200 0 0.02 0.04 0.06 0.08 0.1 K (-20µm) K @ DEC K (+20µm) σ x (-20µm) σ x @ DEC σ x (+20µm) K (MPa*m1/2) σ x (MPa) Y Position (mm) 600 800 1000 1200 1400 K (-20 µm) K @ DEC K (-20 µm) σ x (-20 µm) σ x @ DEC σ x (+20 µm) Figure 4: Stress distribution and resulting K solution for 1 mm thick specimen case. Figure 5: Stress distribution and resulting K solution for 4 mm thick specimen, µ=0.3 case. Figure 6: Stress distribution and resulting K solution for 4 mm thick specimen, µ=1.0 case. Figure 7: Comparison of relative displacements along the contact calculated for all three simulation conditions identified in Table 1. 4 8 12 16 20 0 1 2 4mm, µ = 1.0 4mm, µ = 0.3 1mm, µ = 0.3 Relative Slip (µm) Axial Location (mm) 0 2 4 6 8 10 0 200 400 600 800 1000 1200 1400 0 0.02 0.04 0.06 0.08 0.1 K (- 20µm) K @ DEC K (+ 20µm) σ x (- 20µm) σ x @ DEC σ x (+ 20µm) K (MPa*m1/2) σ x (MPa) Y Position (mm) effect by increasing the stress through an increase in µ rather than through multiplying by relative displacement. To explore this concept the next comparison is of the two cases in which a 4 mm thick specimen with a long pad was modeled with two different values of µ. Increasing µ arbitrarily from 0.3 to 1.0 results in an increase in the maximum σx from ~ 500 MPa (Fig. 5) to 1100 MPa (Fig. 6). A similar increase was noted in the previous investigation of a 2 mm thick specimen [1]. Corresponding increases in maximum shear stresses were also noted for increases in µ, which are not discussed here. As with the previous comparison, the case with µ=1.0 resulting in higher tensile stresses also produced higher K values. Changes in µ also produce changes in relative slip between the pad and specimen. In Figure 7, relative slip is plotted from the DEC, denoted by x=0, to x=2.0 mm under the fretting pad. Maximum slip distance occurs at the edge of contact, which is where the maximum tensile stresses occur. For the 4 mm thick specimen and long pad cases discussed above, the maximum slip distances corresponding to maximum tensile stresses is reduced from 19 µm (500 MPa) to 3.4 µm (1100 MPa). By comparison, the 1 mm thick specimen and short pad case produced a maximum relative slip of 4.0 µm (1300 MPa). These results are consistent with findings from the previous investigation, which concluded that stresses and displacements near the edge of contact are very sensitive to the value of µ between pad and specimen [1].
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