Fig. 1 Qualitative representation of the tensile strength and compressive strength through the Mohr’s stress circles and fracture criterion lines. The diameters of the two Mohr’s circles denote the fracture strength of tension and compression, respectively

Fig. 2 Variation of compressive strength of a <110>, b <111> orientations against <100> orientation with the variation of τ0{111}<112>/σ0{111} of six fcc crystals

Fig. 3 Stereographic contour plots of compressive strength of a Cu, b Au, c Ni, d Pt, e Al, f Ir. Black spots are denoted as the loading orientations where the maximum or minimum compressive strength appears

Fig. 4 Variation of asymmetries between tensile and compressive strength of a <100> orientation (κ<100>) with the variation of τ0{111}<112>/σ0{111} and b <110>, <111> orientations (κ<110> and κ<111>) with the variation of τ0{111}<112>/σ0{110} of six fcc crystals

Fig. 5 Stereographic contour plots of the asymmetry between tensile strength and compressive strength of a Cu, b Au, c Ni, d Pt, e Al, f Ir. Black spots and lines are denoted as the loading orientations where the maximum and minimum t/c asymmetries happen. For further analysis, the orientations where cleavage would happen under tension [26] are encircled with white dashed lines and marked with C (cleavage) inside the circles

Fig. 6 a Percentages of orientations for κ > 1 and κ ≤ 1 among all the orientations of the spatial space b average strength asymmetry (\(\bar{\kappa }\)) of the six fcc crystals