Analytical and finite element analysis of stress concentration factors for polyvinylchloride reinforced with different types of short fibers

	Tensile strength (MPa)	Density (kg/m³)	Fiber diameter (mm)	Modulus of elasticity (MPa)	Poisson’s ratio
PVC www.egy-petrochem.com	40.7	1,300	—	2,366	0.38
Glass fiber type E6-CR	2,400	22	0.013	3,230	0.5
Glass fiber type YGT10	2,100	20	0.011	1919	0.31
GW	3,500	16	0.01	2,211	0.35
RW	—	40	0.15	2,523	0.4
CW	—	25	0.005	1,024	0.16

Table 2

Parameters of the prepared samples.

Fiber content (wt%)	Fiber length (mm)	PVC content (wt%)	Weight of fiber (g)	Weight of PVC (g)
0	—	100	0	250
5	5	95	12.5	237.5
10	5	90	25	225
15	5	85	37.5	212.5
20	5	80	50	200
30	5	70	75	175
40	5	60	100	150
50	5	50	125	125

Typical SEM micrograph of longitudinal distribution of fibers in the PVC sample. (a) SEM micrograph of tensile fracture surface for pure PVC. (b) SEM micrograph of tensile fracture surface for PVC/5% E6-CR composite. (c) SEM micrograph of tensile fracture surface for PVC/30% E6-CR composite. (d) SEM micrograph of tensile fracture surface for PVC/50% E6-CR composite. (e) SEM micrograph of tensile fracture surface for PVC/5% YGT101 composite. (f) SEM micrograph of tensile fracture surface for PVC/20% YGT101 composite. (g) SEM micrograph of tensile fracture surface for PVC/50% YGT101 composite. (h) SEM micrograph of tensile fracture surface for PVC/5% GW composite. (i) SEM micrograph of tensile fracture surface for PVC/15% GW composite. (j) SEM micrograph of tensile fracture surface for PVC/50% GW composite. (k) SEM micrograph of tensile fracture surface for PVC/5% RW composite. (l) SEM micrograph of tensile fracture surface for PVC/15% RW composite. (m) SEM micrograph of tensile fracture surface for PVC/50% RW composite. (n) SEM micrograph of tensile fracture surface for PVC/5% CW composite. (o) SEM micrograph of tensile fracture surface for PVC/15% CW composite. (p) SEM micrograph of tensile fracture surface for PVC/50% CW composite.

Table 3

Tensile strength results for PVC/E6-CR.

Hole diameter (mm)		Fiber content (%)
Hole diameter (mm)		0	5	10	15	20	30	40	50
0	Elastic modulus (MPa)	2221.15	1438.34	2061.64	2340.14	2392.50	2312.54	1794.90	1657.21
	Poison ratio	0.38	0.31	0.28	0.45	0.48	0.37	0.38	0.50
	Tensile strength	37.69	26.81	56.44	28.42	55.94	63.01	29.78	28.15
1	Elastic modulus (MPa)	2184.72	1785.70	1607.13	2571.41	2769.58	2122.30	2153.47	2983.66
	Poison ratio	0.38	0.31	0.28	0.45	0.48	0.37	0.38	0.50
	Tensile strength	38.40	25.97	38.96	46.75	50.36	52.74	26.10	19.89
3	Elastic modulus (MPa)	2619.21	1833.96	1765.99	3178.79	3103.12	1764.90	3141.66	3223.58
	Poison ratio	0.38	0.27	0.26	0.46	0.45	0.26	0.46	0.47
	Tensile strength	31.75	20.01	32.11	38.53	39.49	41.72	22.85	17.58
5	Elastic modulus (MPa)	2487.94	2419.91	1975.44	3111.31	3144.07	2333.51	3015.99	2948.20
	Poison ratio	0.38	0.37	0.30	0.48	3144.07	0.36	0.46	0.45
	Tensile strength	22.62	17.60	25.14	30.17	36.20	39.60	18.28	14.29

Table 4

Tensile strength results for PVC/YGT-101.

Hole diameter (mm)		Fiber content (%)
Hole diameter (mm)		0	5	10	15	20	30	40	50
0	Elastic modulus (MPa)	2221.15	1135.00	1019.01	1199.69	941.77	644.13	2272.72	1489.23
	Poison ratio	0.38	0.33	0.35	0.26	0.18	0.13	0.41	0.31
	Tensile strength	37.69	30.13	30.13	36.68	29.91	16.01	34.08	13.82
1	Elastic modulus (MPa)	2184.72	1871.17	2022.46	1477.01	1037.14	760.77	2330.94	1771.81
	Poison ratio	0.38	0.33	0.35	0.26	0.18	0.13	0.41	0.31
	Tensile strength	38.40	23.81	26.97	30.44	23.26	13.37	22.60	9.66
3	Elastic modulus (MPa)	2619.21	3251.90	2637.39	1591.77	1115.98	1673.97	3117.80	2537.01
	Poison ratio	0.38	0.48	0.38	0.23	0.16	0.24	0.46	0.37
	Tensile strength	31.75	21.68	25.57	24.12	18.26	18.26	18.90	7.69
5	Elastic modulus (MPa)	2487.94	3161.13	3203.51	1792.96	1302.23	1443.15	3221.9	2705.20
	Poison ratio	0.38	0.49	0.49	0.28	0.20	0.22	0.50	0.42
	Tensile strength	22.62	21.07	19.42	19.56	16.57	9.62	15.62	4.92

Table 5

Tensile strength results for PVC/GW.

Hole diameter (mm)		Fiber content (%)
Hole diameter (mm)		0	5	10	15	20	30	40	50
0	Elastic modulus (MPa)	2221.15	1425.04	1050.53	1073.41	711.40	695.70	1804.52	977.31
	Poison ratio	0.38	0.45	0.18	0.24	0.15	0.16	0.42	0.36
	Tensile strength	37.69	37.52	30.74	23.82	26.00	26.00	25.58	8.96
1	Elastic modulus (MPa)	2184.72	2542.70	1039.26	1351.93	877.04	899.31	2426.06	2041.00
	Poison ratio	0.38	0.45	0.18	0.24	0.15	0.16	0.42	0.36
	Tensile strength	38.40	30.82	26.45	22.12	20.20	16.35	22.06	8.66
3	Elastic modulus (MPa)	2619.21	3368.56	1209.73	1706.12	1095.09	1206.18	3025.06	2127.91
	Poison ratio	0.38	0.49	0.18	0.25	0.16	0.18	0.42	0.31
	Tensile strength	31.75	30.62	25.66	19.65	19.25	14.62	20.17	7.74
5	Elastic modulus (MPa)	2487.94	3219.01	1211.84	2299.99	1438.69	1630.33	2559.87	2514.90
	Poison ratio	0.38	0.49	0.19	0.35	0.22	0.25	0.39	0.39
	Tensile strength	22.62	23.41	17.63	15.33	17.44	11.86	13.96	6.86

Table 6

Tensile strength results for PVC/RW.

Hole diameter (mm)		Fiber content (%)
Hole diameter (mm)		0	5	10	15	20	30	40	50
0	Elastic modulus (MPa)	2221.15	911.08	1215.41	906.87	651.38	575.77	1017.71	1652.12
	Poison ratio	0.38	0.20	0.38	0.23	0.14	0.13	0.29	0.41
	Tensile strength	37.69	29.16	23.89	29.45	27.19	19.97	16.26	14.69
1	Elastic modulus (MPa)	2184.72	1157.31	2142.16	1331.86	811.55	726.29	1681.13	2328.97
	Poison ratio	0.38	0.20	0.38	0.23	0.14	0.13	0.29	0.41
	Tensile strength	38.40	25.95	20.77	25.83	19.67	18.05	14.26	14.11
3	Elastic modulus (MPa)	2619.21	1411.28	2776.67	1602.87	1012.67	845.66	2546.65	2376.87
	Poison ratio	0.38	0.21	0.41	0.23	0.15	0.12	0.37	0.35
	Tensile strength	31.75	23.09	20.19	25.26	19.03	16.40	10.80	8.64
5	Elastic modulus (MPa)	2487.94	1485.15	2985.64	2093.17	1336.57	731.58	2114.27	2861.98
	Poison ratio	0.38	0.23	0.46	0.33	0.21	0.11	0.32	0.44
	Tensile strength	22.62	18.00	16.29	24.10	15.39	10.20	7.69	6.94

Table 7

Tensile strength results for PVC/CW.

Hole diameter (mm)		Fiber content (%)
Hole diameter (mm)		0	5	10	15	20	30	40	50
0	Elastic modulus (MPa)	2221.15	910.67	1291.15	1241.47	801.52	547.04	714.74	508.75
	Poison ratio	0.38	0.25	0.25	0.25	0.16	0.11	0.17	0.17
	Tensile strength	37.69	36.47	33.68	33.05	24.41	17.74	19.09	9.85
1	Elastic modulus (MPa)	2184.72	1403.77	1455.48	1443.56	909.13	652.11	949.58	945.86
	Poison ratio	0.38	0.25	0.25	0.25	0.16	0.11	0.17	0.17
	Tensile strength	38.40	32.33	29.11	28.00	22.59	15.41	16.11	8.60
3	Elastic modulus (MPa)	2619.21	1655.48	1801.16	1889.76	1048.34	817.47	1495.58	1596.14
	Poison ratio	0.38	0.24	0.26	0.28	0.15	0.12	0.22	0.23
	Tensile strength	31.75	29.10	26.20	25.20	20.33	13.87	14.50	7.74
5	Elastic modulus (MPa)	2487.94	2267.09	2041.32	2524.17	1140.59	1023.99	2259.99	2713.45
	Poison ratio	0.38	0.35	0.31	0.39	0.18	0.16	0.35	0.42
	Tensile strength	22.62	24.73	22.27	21.42	17.28	11.79	12.33	6.58

Normalized strength for PVC/E6-CR fiber.

Normalized strength for PVC/YGT-101 fiber.

Table 8

Analytical stress concentration solution with different hole diameters.

Hole diameter (mm)	K _t Hywood	K _t Howland
0	3.000	3.004
1	2.852	2.789
3	2.591	2.464
5	2.378	2.255

FEA using Solidworks and ANSYS for hole 1 mm diameter. (a) Solidworks model. (b) ANSYS model. (c) Fixed face for Solidworks model. (d) Fixed face ANSYS model. (e) Tension force for Solidworks. (f) Tension force for ANSYS model. (g) Mesh on Solidworks. (h) Mesh on ANSYS. (i) Maximum stress using Solidworks model. (j) Maximum stress using ANSYS model.

Table 9

Comparison between the analytical method and FEA analysis with different hole diameters.

Material	Hole diameter (mm)	Stress concentration factor				Error based on Howland equation
Material	Hole diameter (mm)	Heywood	Howland	SolidWorks	ANSYS	Solidworks (%)	ANSYS (%)
PVC	1	2.852	2.789	2.611	2.661	6	5
	3	2.592	2.464	2.252	2.380	9	3
	5	2.379	2.255	2.199	2.230	2	1
E6-CR	1	2.852	2.789	2.573	2.665	8	4
	3	2.592	2.464	2.266	2.383	8	3
	5	2.379	2.255	2.206	2.235	2	1
YGT-101	1	2.852	2.789	2.632	2.675	6	4
	3	2.592	2.464	2.270	2.382	8	3
	5	2.379	2.255	2.190	2.229	3	1
GW	1	2.852	2.789	2.631	2.680	6	4
	3	2.592	2.464	2.277	2.383	8	3
	5	2.379	2.255	2.188	2.223	3	1
RW	1	2.852	2.789	2.639	2.681	5	4
	3	2.592	2.464	2.282	2.380	7	3
	5	2.379	2.255	2.193	2.223	3	1
CW	1	2.852	2.789	2.651	2.689	5	4
	3	2.592	2.464	2.288	2.376	7	4
	5	2.379	2.255	2.190	2.222	3	1

Comparison between the analytical method and FEA analysis at hole 1 mm.

Comparison between the analytical method and FEA analysis at hole 3 mm.

Comparison between the analytical method and FEA analysis at hole 5 mm.

Table 10

Comparison between analytical method and FEA analysis for all hole diameters.

Comparison between analytical and FEA for all hole diameters
Hole diameter (mm)	Analytical	Solidworks analysis	ANSYS analysis
1	2.789	2.623	2.675
3	2.464	2.273	2.381
5	2.255	2.194	2.227

References

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DOI: https://doi.org/10.2478/msp-2026-0003 | Journal eISSN: 2083-134X (formerly 2083-124X) | Journal ISSN: 2083-1331

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Language: English

Page range: 30 - 49

Submitted on: Dec 11, 2024

Accepted on: Jan 15, 2026

Published on: Mar 17, 2026

Published by: Wroclaw University of Science and Technology

In partnership with: Paradigm Publishing Services

Keywords:

Composite materials,

Polyvinylchloride (PVC),

Short fiber,

Fiber content,

Open hole tensile test,

Stress concentration factor (SCF),

Finite element analysis (FEA)

Related subjects:

Materials sciences,

Materials sciences, other,

Nanomaterials,

Functional and smart materials,

Materials characterization and properties

© 2026 Yasser S. Mohamed, Hesham A. Ghonem, Wael A. Crosby, published by Wroclaw University of Science and Technology
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 44 (2026): Issue 1 (March 2026)

Analytical and finite element analysis of stress concentration factors for polyvinylchloride reinforced with different types of short fibers

Figures & Tables

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Table 10

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