Multiscale Failure Analysis and Micromechanical Fem Modeling of Type IV Composite Pressure Vessel Considering Different Fibre Shapes and Dehomogenisation

MUŚKO, Piotr; PERKOWSKI, Dariusz M.

doi:10.2478/ama-2025-0071

Figures & Tables

Construction of composite pressure vessel type IV

Scan of the actual fibre structure: a) multifiber view, b) single fibre zoom

a) RVE with circular fibre: b) RVE with elliptical fibre

RVE with actual fibre: a) geometry, b) mesh

Displacement distributions of RVE: a) tensile in X-direction, b) tensile in Y-direction, c) tensile in Z-direction

Displacement distributions of RVE: a) shear in XY-plane, b) shear in XZ-plane, c) shear in YZ-plane

Equivalent stress distributions of RVE: a) tensile X-direction, b) tensile Y-direction, c) tensile Z-direction

Equivalent stress distributions of RVE: a) shear in XY-plane, b) shear in XZ-plane, c) shear in YZ-plane

Model displacements to calculate Young's modulus, Poisson's ratio and shear modulus

Solid model of composite pressure vessel

Composite thickness distribution at dome section for first 8 helical layers

Thickness distribution of composite at dome part in 3D model: a) Wang method, b) numerical model

Quality of finite elements mesh graph: a) aspect ratio, b) element quality, c) skewness d) Jacobian ratio

Distribution of resultant: a) displacement b) strain

Distribution of Huber von-Mises stress in a) closed boss b) open boss [MPa]

Distribution of Huber von-Mises stress in the polyamide liner [MPa]

Puck failure distribution: a) fibre, b) matrix

Hashin failure distribution: a) fibre, b) matrix

Stress distributions for maximum Puck fibre failure criterion strains: a) Equivalent Huber von-Mises stress for RVE, b) normal X-direction stress for fibre, c) Equivalent Huber von-Mises stress for matrix

Stress distributions for maximum Puck matrix failure criteria strains: a) Equivalent Huber von-Mises stress for RVE, b) normal X-direction stress for fibre, c) Equivalent Huber von-Mises stress for matrix

Stress distributions for maximum Hashin fibre failure criteria strains: a) Equivalent Huber von-Mises stress for RVE, b) normal X-direction stress for fibre, c) Equivalent Huber von-Mises stress for matrix

Stress distributions for maximum Hashin matrix failure criteria strains: a) Equivalent Huber von-Mises stress for RVE, b) normal X-direction stress for fibre, c) Equivalent Huber von-Mises stress for matrix

Stress distributions for maximum Tsai Wu failure criteria strains: a) Equivalent Huber von-Mises stress for RVE, b) normal X-direction stress for fibre, c) Equivalent Huber von-Mises stress for matrix

Maximum values of damage index for each winding angle layer

Angle [°]	Failure
10	0,759
14,5	0,547
19	0,678
23	0,498
27,5	0,536
31,5	0,566
36,5	0,581
>90	0,580

Displacement conditions for walls

Surface X = 0	Surface Y = 0	Surface Z = 0
u(0,y,z) = ε_xy 1 ε._xzzv(0,y,z) = ε_yyy + ε_yzzw(0,y,z) = ε_yzy + ε_zzz	u(x, 0, z) = ε_xxx + ε_xzzv(x, 0, z) = ε_xyx + ε_yzzw(x, 0, z) = ε_xzx + ε_zzz	u(x,y,0) = ε_xxx + ε_xyyv(x,y,0) = ε_xyx + ε_yyyw(x,y,0) = ε_xzx + ε_yzy
Surface X = L_x	Surface Y = L_x	Surface Z = L_x
u(L_x,y,z) = ε_xxL_x + ε_xyy + ε_xzzv(L_x,y,z) = ε_xyε_x + ε_yyy + ε_yzZw(L_x,y,z) = ε_xzL_x + ε_yzy + ε_zzz	u(x, L_y, z) = ε_xxx + ε_xyL_y + ε_xzzv(x, L_y, z) = ε_xyx + ε_yyL_y + ε_yzzw(x, L_y, z) = ε_xzx + ε_yzL_y + ε_zzz	u(x,y,L_z) = ε_xxx + ε_xyy + ε_xzL_zv(x,y,L_z) = ε_xyx + ε_yyy + ε_yzL_zw(x,y,L_z) = ε_xzx + ε_yzy + ε_zzL_z

PBC equations for shear in XZ-plane

Surfaces	Edges	Vertices
ux3478−ux1256=0u_x^{3478} - u_x^{1256} = 0	ux34−ux12=0,ux78−ux56=0\matrix{ {u_x^{34} - u_x^{12} = 0,} \hfill & {u_x^{78} - u_x^{56} = 0} \hfill \cr }	ux4−ux1=0u_x^4 - u_x^1 = 0
uy2367−uy1458=0u_y^{2367} - u_y^{1458} = 0	uy37−uy48=0,uy26−uy15=0uy23−uy14=0,uy67−uy58=0\matrix{ {u_y^{37} - u_y^{48} = 0,} \hfill & {u_y^{26} - u_y^{15} = 0} \hfill \cr {u_y^{23} - u_y^{14} = 0,} \hfill & {u_y^{67} - u_y^{58} = 0} \hfill \cr }	uy3−uy4=0,uy2−uy1=0uy6−uy5=0,uy7−uy8=0\matrix{ {u_y^3 - u_y^4 = 0,} \hfill & {u_y^2 - u_y^1 = 0} \hfill \cr {u_y^6 - u_y^5 = 0,} \hfill & {u_y^7 - u_y^8 = 0} \hfill \cr }
uz5678−uz1234=0u_z^{5678} - u_z^{1234} = 0	uz78−uz34=0,uz56−uz12=0\matrix{ {u_z^{78} - u_z^{34} = 0,} \hfill & {u_z^{56} - u_z^{12} = 0} \hfill \cr }	uz5−uz1=0u_z^5 - u_z^1 = 0

PBC equations for shear in YZ-plane

Surfaces	Edges	Vertices
ux5678−ux1234=0u_x^{5678} - u_x^{1234} = 0	ux58−ux14=0,ux67−ux23=0ux78−ux34=0,ux56−ux12=0\matrix{ {u_x^{58} - u_x^{14} = 0,} \hfill & {u_x^{67} - u_x^{23} = 0} \hfill \cr {u_x^{78} - u_x^{34} = 0,} \hfill & {u_x^{56} - u_x^{12} = 0} \hfill \cr }	ux5−ux1=0,ux6−ux2=0ux8−ux4=0,ux7−ux3=0\matrix{ {u_x^5 - u_x^1 = 0,} \hfill & {u_x^6 - u_x^2 = 0} \hfill \cr {u_x^8 - u_x^4 = 0,} \hfill & {u_x^7 - u_x^3 = 0} \hfill \cr }
uy3478−uy1256=0u_y^{3478} - u_y^{1256} = 0	uy48−uy15=0,uy37−uy26=0\matrix{ {u_y^{48} - u_y^{15} = 0,} \hfill & {u_y^{37} - u_y^{26} = 0} \hfill \cr }	uy4−uy1=0u_y^4 - u_y^1 = 0
uz2367−uz1458=0u_z^{2367} - u_z^{1458} = 0	uz26−uz15=0,uz37−uz48=0\matrix{ {u_z^{26} - u_z^{15} = 0,} \hfill & {u_z^{37} - u_z^{48} = 0} \hfill \cr }	uz2−uz1=0u_z^2 - u_z^1 = 0

PBC equations for shear in XY-plane

Surfaces	Edges	Vertices
ux2367−ux1458=0u_x^{2367} - u_x^{1458} = 0	ux23−ux14=0,ux67−ux58=0\matrix{ {u_x^{23} - u_x^{14} = 0,} \hfill & {u_x^{67} - u_x^{58} = 0} \hfill \cr }	ux2−ux1=0u_x^2 - u_x^1 = 0
uy5678−uy1234=0u_y^{5678} - u_y^{1234} = 0	uy67−uy23=0,uy58−uy14=0\matrix{ {u_y^{67} - u_y^{23} = 0,} \hfill & {u_y^{58} - u_y^{14} = 0} \hfill \cr }	uy5−uy1=0u_y^5 - u_y^1 = 0
uz3478−uz1256=0u_z^{3478} - u_z^{1256} = 0	uz48−uz15=0,uz37−uz26=0uz34−uz12=0,uz78−uz56=0\matrix{ {u_z^{48} - u_z^{15} = 0,} \hfill & {u_z^{37} - u_z^{26} = 0} \hfill \cr {u_z^{34} - u_z^{12} = 0,} \hfill & {u_z^{78} - u_z^{56} = 0} \hfill \cr }	uz4−uz1=0,uz3−uz2=0uz7−uz6=0,uz8−uz5=0\matrix{ {u_z^4 - u_z^1 = 0,} \hfill & {u_z^3 - u_z^2 = 0} \hfill \cr {u_z^7 - u_z^6 = 0,} \hfill & {u_z^8 - u_z^5 = 0} \hfill \cr }

Layup configuration

Number of layers	Angle [°]	Quantity
2	10	x₂
3	90
1	14,5
1	19
3	90
1	23
1	27,5
3	90
1	31,5
1	36,5
3	90
2	10	x₂
3	90
1	14,5
1	19
3	90
1	23
1	27,5
3	90
2	10	x₁

Strain values in the most loaded elements

Failure criteria/strain	ε_xx	ε_yy	ε_zz	ε_xy	ε_xz	ε_yz
Puck fibre	7,986 · 10⁻³	–1,011 · 10⁻²	2,073 · 10⁻³	–9,570 · 10⁻⁵	2,034 · 10⁻⁴	6,786 · 10⁻⁴
Puck matrix	4,521 · 10–3	2,370 · 10⁻³	–3,099 · 10⁻³	–8,194 · 10⁻³	–8,872 · 10⁻³	3,176 · 10⁻³
Hashin fibre	2,230 · 10–3	–6,224 · 10⁻³	–5,999 · 10⁻³	1,383 · 10⁻²	1,201 · 10⁻³	8,919 · 10⁻³
Hashin matrix	4,522 · 10⁻³	2,370 · 10⁻³	–3,098 · 10⁻³	–8,194 · 10⁻³	–8,875 · 10⁻³	3,171 · 10⁻³
Tsai Wu	4,521 · 10⁻³	2,370 · 10⁻³	–3,099 · 10⁻³	–8,194 · 10⁻³	–8,872 · 10⁻³	3,176 · 10⁻³

Mechanical strength properties of carbon epoxy composite

Properties	Values [MPa]
Longitudinal Tensile Strength X_t	2860
Transverse Tensile Strength Y_t,Z_t	81
Longitudinal Compressive Strength X_c	-1450
Transverse Compressive Strength Y_c,Z_c	-268,5
Shear Strength in fiber plane S₁₂, S₁₃	136
Sherar strength out of fiber plane S₂₃	87

Mechanical properties of carbon fibre and resin epoxy

Carbon fiber T700 (9)		Epoxy resin (9)
Properties	Values	Properties	Values
E_x[GPa]	230	Tensile modulus E_m[GPa]	>3,2
E_y, E_z[GPa]	28	Tensile modulus E_m[GPa]	>3,2
G_xy, G_xz[GPa]	50	Shear modulus G_m[GPa]	1,17
G_yz[GPa]	10	Shear modulus G_m[GPa]	1,17
v_xy, v_xz	0,23	Poisson’s ratio v_m	0,35
v_yz	0,3	Poisson’s ratio v_m	0,35

Mechanical properties of 6061 and PA6 [23, 24]

Properties	6061-T6	PA6
Tensile Modulus [GPa]	68,9	1,4
Poisson's ratio	0,33	0,35
Yield Strength [MPa]	276	76
Tensile Strength [MPa]	310	-

Winding angles correspond to variable polar radius for helical layers

Winding angleα [°]	Total number of layers	Radius of polar openings r₀ [mm]
10	10	30
14,5	4	42
19	4	54
23	4	66
27,5	4	78
31,5	2	90
36,5	2	102

Mechanical properties of carbon epoxy composite

Properties	Material Designer (Circular fibre)	PBC equations in Mechanical			Difference between actual fibre and circular fibre [%]
Properties	Material Designer (Circular fibre)	Circular fibre	Eliptical fibre	Actual fibre	Difference between actual fibre and circular fibre [%]
E₁[GPa]	139,345	139,012	138,972	142,502	2,51
E₂[GPa]	8,242	8,195	8,291	8,612	5,09
E₃[GPa]	8,242	8,195	8,288	8,620	5,19
G₁₂[GPa]	4,657	4,629	4,900	5,122	10,65
G₂₃[GPa]	3,943	3,936	4,454	4,153	5,51
G₁₃[GPa]	4,657	4,629	4,899	5,143	11,10
v₁₂	0,271	0,271	0,272	0,270	0,37
v₂₃	0,501	0,494	0,468	0,466	6,99
v₁₃	0,271	0,271	0,272	0,270	0,37

PBC equations for tensile in X, Y, and Z direction

Surfaces	Edges	Vertices
ux5678−ux1234=0u_x^{5678} - u_x^{1234} = 0	ux56−ux12=0,ux78−ux34=0,ux58−ux14=0,ux67−ux23=0\matrix{ {u_x^{56} - u_x^{12} = 0,} \hfill & {u_x^{78} - u_x^{34} = 0,} \hfill \cr {u_x^{58} - u_x^{14} = 0,} \hfill & {u_x^{67} - u_x^{23} = 0} \hfill \cr }	ux5−ux1=0,ux6−ux2=0,ux8−ux4=0,ux7−ux3=0\matrix{ {u_x^5 - u_x^1 = 0,} \hfill & {u_x^6 - u_x^2 = 0,} \hfill \cr {u_x^8 - u_x^4 = 0,} \hfill & {u_x^7 - u_x^3 = 0} \hfill \cr }
uy2367−uy1458=0u_y^{2367} - u_y^{1458} = 0	uy23−uy14=0,uy67−uy58=0,uy26−uy15=0,uy37−uy48=0\matrix{ {u_y^{23} - u_y^{14} = 0,} \hfill & {u_y^{67} - u_y^{58} = 0,} \hfill \cr {u_y^{26} - u_y^{15} = 0,} \hfill & {u_y^{37} - u_y^{48} = 0} \hfill \cr }	uy2−uy1=0,uy6−uy5=0,uy3−uy4=0,uy7−uy8=0\matrix{ {u_y^2 - u_y^1 = 0,} \hfill & {u_y^6 - u_y^5 = 0,} \hfill \cr {u_y^3 - u_y^4 = 0,} \hfill & {u_y^7 - u_y^8 = 0} \hfill \cr }
uz3478−uz1256=0u_z^{3478} - u_z^{1256} = 0	uz78−uz56=0,uz34−uz12=0,uz48−uz15=0,uz37−uz26=0\matrix{ {u_z^{78} - u_z^{56} = 0,} & {u_z^{34} - u_z^{12} = 0,} \cr {u_z^{48} - u_z^{15} = 0,} & {u_z^{37} - u_z^{26} = 0} \cr }	uz4−uz1=0,uz8−uz5=0,uz7−uz6=0,uz3−uz2=0]\matrix{ {u_z^4 - u_z^1 = 0,} \hfill & {u_z^8 - u_z^5 = 0,} \hfill \cr {u_z^7 - u_z^6 = 0,} \hfill & {u_z^3 - u_z^2 = 0} \hfill \cr }

Maximum stress results from dehomogenisation for different fibre geometries

Failure criteria	Stress limit [MPa]		Circular fibre			Eliptical fibre			Actual fibre
Failure criteria	fibre	resin	RVE	fibre	resin	RVE	fibre	resin	RVE	fibre	resin
Puck fibre	4900	80	1868	1832,9	89,9	1795,4	1760	90,5	1923	1820	133,4
Puck matrix			1104,8	1128,1	57	1027,4	1067	55,1	1095,6	1133,6	76,3
Hashin fibre			676,1	553,2	154,4	680,9	563,35	177,2	1110,7	580,2	238,3
Hashin matrix			1104,9	1128,2	57	1107,9	1120,3	53,9	1188,9	1204,5	138,7
Tsai wu			1104,8	1128,1	57	1107,8	1120,2	54	1188,8	1204,4	138,7

Multiscale Failure Analysis and Micromechanical Fem Modeling of Type IV Composite Pressure Vessel Considering Different Fibre Shapes and Dehomogenisation

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Maximum values of damage index for each winding angle layer

Displacement conditions for walls

PBC equations for shear in XZ-plane

PBC equations for shear in YZ-plane

PBC equations for shear in XY-plane

Layup configuration

Strain values in the most loaded elements

Mechanical strength properties of carbon epoxy composite

Mechanical properties of carbon fibre and resin epoxy

Mechanical properties of 6061 and PA6 [23, 24]

Winding angles correspond to variable polar radius for helical layers

Mechanical properties of carbon epoxy composite

PBC equations for tensile in X, Y, and Z direction

Maximum stress results from dehomogenisation for different fibre geometries