Burst tests and pressure calculations for PVC⁃UH pipes with various diameters

doi:10.19491/j.issn.1001-9278.2025.09.015

Abstract

Abstract:

In this study， the burst pressure calculation methods for PVC⁃UH pipes were investigated through experimental and theoretical analysis. Burst tests were conducted on four types of small⁃to⁃medium diameter pipes to evaluate the applicability and accuracy of various burst pressure calculation theories. Based on the material characteristics of PVC⁃UH， a new calculation method was proposed using a plastic deformation criterion. The results indicated that conventional metal pipe formulas were unsuitable for PVC⁃UH pipes. When using nominal yield strength as the calculation parameter， the TSSY criterion， modified Nadai， Bailey⁃Nadai， Welling⁃Uebing， Turner， Bailey， ASME， Barlow series， maximum stress guidelines， maximum shear stress guidelines， and Zhu⁃Leis method are appropriate. For true breaking strength， the Tresca criterion， Marin⁃2， Svenson， Bohm， and API methods are recommended. The most accurate results were obtained using the average of nominal yield strength and true fracture strength. A 0.4 % residual strain failure criterion was proposed， which demonstrated through twofold elastic deformation analysis that PVC⁃UH pipes fail at 1.7 % circumferential strain. The derived plastic deformation⁃based formula shows excellent agreement with experimental data， providing reliable technical support and theoretical basis for PVC⁃UH pipe burst pressure calculation.

Key words: poly（vinyl chloride）, pipe, burst pressure, calculation comparison, plastic deformation failure criterion

CLC Number:

TQ325.4

LI Wei, TANG Pengfei, PAN Dong, SHI Tuo, MO Shubei. Burst tests and pressure calculations for PVC⁃UH pipes with various diameters[J]. China Plastics, 2025, 39(9): 93-100.

Figures/Tables 12

Fig.1. Testing pipe of dn630t24

Fig.2. Strain gauges arrangement of pipe wall

Fig.3. The yield surfaces of the unified strength theory

公式名称	表达式	备注
Nadai	$P = 23 σ T S' l n k$	基于管壁全截面屈服和Mises准则，主要用于厚壁圆筒。 $k$ 为管道外内径比。
修正的Nadai	$P = σ T S' 3 n 1 - 1 k 2 n$	考虑材料硬化特性。
Bailey⁃Nadai	$P = σ T S' 2 n 1 - 1 k 2 n$	-
Marin⁃1	$P = 2.31 · 0 . 577 n t σ T S' D i$	考虑材料和管径，主要针对薄壁圆筒， $D i$ 和 $t$ 分别是管道内径和壁厚。
Marin⁃2	$P = 23 σ T S' 1 + n l n k$	主要针对厚壁圆筒。
Marin⁃3	$P = 2 t 3 n + 1 2 σ T S' D i$	主要针对厚壁圆筒。
Marin⁃Rimrot	$P = 23 σ T S' 1 + ε T S' l n k$	考虑材料名义拉伸应力应变及外内径比， $ε T S'$ 为 $σ T S'$ 对应的名义应变。
Soderberg	$P = 43 σ T S' k - 1 k + 1$	-
Faupel	$P = 23 σ Y S' 2 - Y T l n k$	考虑屈强比的半经验公式， $Y T$ 为材料名义屈强比， $Y T = σ Y S' / σ T S'$ ， $σ Y S'$ 为材料名义屈服强度。
Wellinger⁃Uebing	$P = 1.1 σ T S 1 + 2.4 ε T S l n k$	根据材料真实拉伸强度和应变， $σ T S$ 为材料真实拉伸强度， $ε T S$ 为 $σ T S$ 对应的真实应变。
Svensson	$P = σ T S' 0.25 0.227 + n e n n l n k$	根据材料硬化特性的半经验公式，e为自然常数。
Bohm	$P = σ T S 0.25 0.25 + n e n n 2 t D i 1 - t D i$	-
API	$P = 0.875 2 t σ Y S' D$	美国石油协会采用。
Turner	$P = σ T S' l n k$	-
Bailey	$P = σ T S' 2 n 1 - 1 k 2 n$	-
ASME	$P = σ T S' k - 1 0.6 k + 0.4, k ≤ 1.5 σ T S' k 2 - 1 k 2 + 1, k > 1.5$	美国机械工程师学会采用。
Barlow⁃1	$P = σ T S' 2 t D 0$	$D o$ 为管道外径。
Barlow⁃2	$P = σ T S' 2 t D i$	-
Barlow⁃3	$P = σ f l o w 2 t D i$	$σ f l o w$ 为流变应力， $σ f l o w = σ T S' - σ Y S' / 2$ 。
DNV⁃1	$P = σ f l o w 2 t D$	挪威船级社采用。
DNV⁃2	$P = 2 t D - t · σ T S' 1.15 · 23 = 2.01 t · σ T S' D - t$	$D$ 为管道公称直径。
Fletcher	$P = 2 t σ f l o w D i 1 - ε T S 2$	-
最大应力准则	$P = σ T S k - 1$
最大剪应力准则	$P = 2 σ T S k - 1 k + 1$

公式名称	表达式	备注
Nadai	$P = 23 σ T S' l n k$	基于管壁全截面屈服和Mises准则，主要用于厚壁圆筒。 $k$ 为管道外内径比。
修正的Nadai	$P = σ T S' 3 n 1 - 1 k 2 n$	考虑材料硬化特性。
Bailey⁃Nadai	$P = σ T S' 2 n 1 - 1 k 2 n$	-
Marin⁃1	$P = 2.31 · 0 . 577 n t σ T S' D i$	考虑材料和管径，主要针对薄壁圆筒， $D i$ 和 $t$ 分别是管道内径和壁厚。
Marin⁃2	$P = 23 σ T S' 1 + n l n k$	主要针对厚壁圆筒。
Marin⁃3	$P = 2 t 3 n + 1 2 σ T S' D i$	主要针对厚壁圆筒。
Marin⁃Rimrot	$P = 23 σ T S' 1 + ε T S' l n k$	考虑材料名义拉伸应力应变及外内径比， $ε T S'$ 为 $σ T S'$ 对应的名义应变。
Soderberg	$P = 43 σ T S' k - 1 k + 1$	-
Faupel	$P = 23 σ Y S' 2 - Y T l n k$	考虑屈强比的半经验公式， $Y T$ 为材料名义屈强比， $Y T = σ Y S' / σ T S'$ ， $σ Y S'$ 为材料名义屈服强度。
Wellinger⁃Uebing	$P = 1.1 σ T S 1 + 2.4 ε T S l n k$	根据材料真实拉伸强度和应变， $σ T S$ 为材料真实拉伸强度， $ε T S$ 为 $σ T S$ 对应的真实应变。
Svensson	$P = σ T S' 0.25 0.227 + n e n n l n k$	根据材料硬化特性的半经验公式，e为自然常数。
Bohm	$P = σ T S 0.25 0.25 + n e n n 2 t D i 1 - t D i$	-
API	$P = 0.875 2 t σ Y S' D$	美国石油协会采用。
Turner	$P = σ T S' l n k$	-
Bailey	$P = σ T S' 2 n 1 - 1 k 2 n$	-
ASME	$P = σ T S' k - 1 0.6 k + 0.4, k ≤ 1.5 σ T S' k 2 - 1 k 2 + 1, k > 1.5$	美国机械工程师学会采用。
Barlow⁃1	$P = σ T S' 2 t D 0$	$D o$ 为管道外径。
Barlow⁃2	$P = σ T S' 2 t D i$	-
Barlow⁃3	$P = σ f l o w 2 t D i$	$σ f l o w$ 为流变应力， $σ f l o w = σ T S' - σ Y S' / 2$ 。
DNV⁃1	$P = σ f l o w 2 t D$	挪威船级社采用。
DNV⁃2	$P = 2 t D - t · σ T S' 1.15 · 23 = 2.01 t · σ T S' D - t$	$D$ 为管道公称直径。
Fletcher	$P = 2 t σ f l o w D i 1 - ε T S 2$	-
最大应力准则	$P = σ T S k - 1$
最大剪应力准则	$P = 2 σ T S k - 1 k + 1$

Tab.1. Commonly used calculation formula of burst pressure of pipe

公式名称	表达式	备注
Margetson	$P = 4 t D i 3 σ T S' e x p - 2 ε T S 1 + v s e c a n t 3$	考虑泊松比 $v$
Klever⁃Stewart	$P = 2 σ T S' t D o - t 12 1 + n + 13 1 + n$	-
Zhu⁃Leis	$P = 2 + 3 43 1 + 0.239 1 Y T - 1 0.596 4 t σ T S' D$	基于ASSY的修正公式

公式名称	表达式	备注
Margetson	$P = 4 t D i 3 σ T S' e x p - 2 ε T S 1 + v s e c a n t 3$	考虑泊松比 $v$
Klever⁃Stewart	$P = 2 σ T S' t D o - t 12 1 + n + 13 1 + n$	-
Zhu⁃Leis	$P = 2 + 3 43 1 + 0.239 1 Y T - 1 0.596 4 t σ T S' D$	基于ASSY的修正公式

Tab.2. Calculation formula of burst pressure based on ASSY

Fig.4. Comparison of constitutive relationship between metal and PVC

编号	试件型号	试件1	试件2	试件3	试件4	平均值
1	dn110t4.3	3.96	4.06	3.84	4.20	4.02
2	dn160t6.2	4.07	3.72	4.63	-	4.14
3	dn200t8.2	3.90	4.14	4.33	4.25	4.16
4	Dn630t24	3.85	4.23	-	-	4.04

Tab.3. Bursting pressure of testing pipes

计算方式	DN110t4.3		DN160t6.2		DN200t8.2		M_e/%
计算方式	P/MPa	误差/%	P/MPa	误差/%	P/MPa	误差/%	M_e/%
试验值	4.02	-	4.14	-	4.16	-	-
TSSY	3.92	-2.5	3.89	-6.0	4.13	-0.7	3.1
Tresca	2.29	-43.0	2.27	-45.2	2.41	-42.1	43.4
Von Mises	3.00	-25.4	2.97	-28.3	3.15	-24.3	26.0
ASSY	2.64	-34.3	2.61	-37.0	2.78	-33.2	34.8
Nadai	4.55	13.2	4.55	9.9	5.08	22.1	15.1
修正Nadai	3.95	-1.7	3.95	-4.6	4.40	5.8	4.0
Bailey⁃Nadai	3.69	-8.2	3.69	-10.9	4.11	-1.2	6.8
Marin⁃1	3.12	-22.4	3.09	-25.4	3.29	-20.9	22.9
Marin⁃2	2.45	-39.1	2.45	-40.8	2.73	-34.4	38.1
Marin⁃3	3.12	-22.4	3.09	-25.4	3.29	-20.9	22.9
Marin⁃Rimrot	1.98	-50.7	1.98	-52.2	2.21	-46.9	49.9
Soderberg	4.49	11.7	4.49	8.5	5.08	22.1	14.1
Faupel	6.02	49.8	6.02	45.4	6.72	61.5	52.2
Wellinger⁃Uebing	4.12	2.5	4.12	-0.5	4.60	10.6	4.5
Svensson	2.44	-39.3	2.44	-41.1	2.72	-34.6	38.3
Bohm	2.49	-38.1	2.49	-39.9	2.66	-36.1	38.0
API	2.47	-38.6	2.44	-41.1	2.59	-37.7	39.1
Turner	3.94	-2.0	3.94	-4.8	4.40	5.8	4.2
Bailey	3.69	-8.2	3.69	-10.9	4.11	-1.2	6.8
ASME	3.91	-2.7	3.91	-5.6	4.37	5.1	4.5
Barlow⁃1	4.00	-0.5	3.97	-4.1	4.20	-1.0	1.9
Barlow⁃2	4.34	8.0	4.30	3.9	4.57	9.9	7.3
Barlow⁃3	3.64	-9.5	3.60	-13.0	3.83	-7.9	10.1
DNV⁃1	3.49	-13.2	3.46	-16.4	3.67	-11.8	13.8
DNV⁃2	4.36	8.5	4.32	4.3	4.50	8.2	7.0
Fletcher	6.38	58.7	6.32	52.7	6.72	61.5	57.6
最大应力准则	4.25	5.7	4.25	2.7	4.79	15.1	7.8
最大剪应力准则	4.04	0.5	4.04	-2.4	4.57	9.9	4.3
Margetson	4.70	16.9	4.66	12.6	4.95	19.0	16.2
Klever⁃Stewart	2.64	-34.3	2.62	-36.7	2.78	-33.2	34.7
Zhu⁃Leis	4.08	1.5	4.04	-2.4	4.29	3.1	2.3

Tab.4. The burst pressure was calculated by replacing σTS' with the nominal yield strength of PVC⁃UH

计算方式	DN110t4.3		DN160t6.2		DN200t8.2		M_e/%
计算方式	P/MPa	误差/%	P/MPa	误差/%	P/MPa	误差/%	M_e/%
试验值	4.02	-	4.14	-	4.16	-	-
TSSY	6.58	63.7	6.66	60.9	7.08	70.2	64.9
Tresca	3.84	-4.5	3.89	-6.0	4.136	-0.6	3.7
Von Mises	5.03	25.1	5.10	23.2	5.41	30.0	26.1
ASSY	4.43	10.2	4.49	8.5	4.77	14.7	11.1
Nadai	7.82	94.5	7.82	88.9	8.74	110.1	97.8
修正Nadai	6.80	69.2	6.80	64.3	7.56	81.7	71.7
Bailey⁃Nadai	6.34	57.7	6.34	53.1	7.06	69.7	60.2
Marin⁃1	5.24	30.3	5.32	28.5	5.66	36.1	31.6
Marin⁃2	4.21	4.7	4.21	1.7	4.70	13.0	6.5
Marin⁃3	5.24	30.3	5.32	28.5	5.66	36.1	31.6
Marin⁃Rimrot	3.40	-15.4	3.40	-17.9	3.79	-8.9	14.1
Soderberg	7.72	92.0	7.72	86.5	8.74	110.1	96.2
Faupel	6.60	64.2	6.60	59.4	7.37	77.2	66.9
Wellinger⁃Uebing	2.43	-39.6	2.43	-41.3	2.72	-34.6	38.5
Svensson	4.19	4.2	4.19	1.2	4.68	12.5	6.0
Bohm	4.29	6.7	4.29	3.6	4.58	10.1	6.8
API	3.77	-6.2	3.74	-9.7	3.97	-4.6	6.8
Turner	6.78	68.7	6.78	63.8	7.57	82.0	71.5
Bailey	6.34	57.7	6.34	53.1	7.06	69.7	60.2
ASME	6.72	67.2	6.72	62.3	7.51	80.5	70.0
Barlow⁃1	6.88	71.1	6.82	64.7	7.22	73.6	69.8
Barlow⁃2	7.46	85.6	7.39	78.5	7.86	88.9	84.3
Barlow⁃3	5.98	48.8	5.92	43.0	6.30	51.4	47.7
DNV⁃1	5.74	42.8	5.68	37.2	6.03	45.0	41.7
DNV⁃2	7.50	86.6	7.43	79.5	7.90	89.9	85.3
Fletcher	10.49	160.9	9.73	135.0	10.99	164.2	153.4
最大应力准则	7.04	75.1	7.04	70.0	7.92	90.4	78.5
最大剪应力准则	6.69	66.4	6.69	61.6	7.57	82.0	70.0
Margetson	1.95	-51.5	1.81	-56.3	2.06	-50.5	52.8
Klever⁃Stewart	4.55	13.2	4.51	8.9	4.78	14.9	12.3
Zhu⁃Leis	6.87	70.9	6.81	64.5	7.22	73.6	69.7

Tab.5. The burst pressure was calculated by replacing σTS' with the true breaking strength of PVC⁃UH

Fig.5. Analysis of relative error of various calculation methods under two replacement method

编号	实测平均值/MPa	两倍弹性斜率准则	双切线准则	零曲率准则	两倍弹性变形准则	0.2 %残余应变准则	0.4 %残余应变准则
1	4.02	4.47	4.38	4.48	4.13	3.72	4.05
2	4.14	4.43	4.25	4.45	4.07	3.70	4.02
3	4.16	4.70	4.73	4.47	4.34	3.96	4.29
M_e/%	-	10.4	8.4	8.8	2.9	7.6	2.3

Tab.6. Comparison of predicted values by various strain failure criteria

Fig.6. The burst pressure and the corresponding hoop strain are predicted by two criteria

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