The following strain state exists at a point in the neck region of the socket adapter (E = (SN +100) GPa, ν = 0.3) as il

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The following strain state exists at a point in the neck region
of the socket adapter (E = (SN +100) GPa, ν = 0.3) as illustrated
in Figure 1. εx = 800×10-6 , εy = 200×10-6 , εz = -500×10-6 , εxy =
200×10-6 and εzy = -2×SN×10-6 . Where SN = 56

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2.1 Calculate the general stress state for the strains above and
write it in matrix form. [9]
2.2 Calculate the principal stresses. [6]
2.3 Determine the safety factor for the measured stress state
(for both the von Mises and Tresca criteria) if the yield strength
is 300 MPa. [6]
2.4 For a SN Curve as shown (Figure 2) estimate the fatigue life
(assume that the current stress distribution is fully reversed for
each load cycle). [5]

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2.5 Calculate the first invariant of the strain tensor. Does it
have any specific significance?
Stress Amplitude (MPa) 600 500 400 300 200 100 0 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 Cycles to failure 1.E+06 1.E+07 1.E+08