Collapse Pressure Analysis of Transversely Isotropic Thick-Walled Cylinder Using Lebesgue Strain Measure and Transition Theory

Table 4

The pressure required for initial yielding and fully plastic state for transversely isotropic material (magnesium).

Magnesium (transversely isotropic material)
Pressure	𝑃𝑖/𝑃𝑓	𝑎/𝑏=0.2	𝑎/𝑏=0.3	𝑎/𝑏=0.4	𝑎/𝑏=0.5	((𝑃𝑓−𝑃𝑖)/𝑃𝑓)∗100
						𝑎/𝑏=0.2	𝑎/𝑏=0.3	𝑎/𝑏=0.4	𝑎/𝑏=0.5
Effective pressure	𝑃𝑖	1.0598	0.87527	0.7164	0.574248	51.8626	37.5544	27.9018	20.7052
	𝑃𝑓	1.60944	1.20397	0.91629	0.693147
Internal pressure = 0	𝑃𝑖	1.0598	0.87527	0.7164	0.574248	51.8626	37.5544	27.9018	20.7052
	𝑃𝑓	1.60944	1.20397	0.91629	0.693147
Internal pressure = 10	𝑃𝑖	8.9402	9.12473	9.2836	9.42575	6.14796	3.6023	2.15315	1.26144
	𝑃𝑓	8.39056	8.79603	9.08371	9.30685
Internal pressure = 50	𝑃𝑖	48.9402	49.1247	49.2836	49.4258	1.123	0.66911	0.40561	0.24056
	𝑃𝑓	48.3906	48.796	49.0837	49.3069

Where 𝑃_𝑖 and 𝑃_𝑓 are pressures required for initial yielding, fully plastic state, while 𝑎 and 𝑏 are internal and external radius of thick-walled circular cylinder.