A novel dual-hardening viscoelastic-plastic constitutive model for thermoplastic resins

doi:10.1007/s10483-026-3354-8

摘要/Abstract

Abstract:

This study examines the viscoelastic-plastic behavior of thermoplastic resin poly-ether-ether-ketone (PEEK) under high temperature and strain rate conditions, highlighting its potential in aerospace applications due to its impact resistance. A dual-hardening constitutive model that combines physical and phenomenological approaches is developed to simulate the mechanical behavior of PEEK. The model explicitly incorporates its marked tension-compression asymmetry in plasticity and relaxation, along with thermal softening at high strain rates, enabling accurate predictions over a wide range of temperatures and strain rates with minimal parameters. This study establishes a comprehensive workflow from experimentation to finite element (FE) simulation for thermoplastic resins. Uniaxial tensile and compression tests (23 °C–180 °C, 0.002 29 s^-1–0.193 61 s^-1) and split Hopkinson pressure bar (SHPB) tests (1 094.08 s^-1–5 957.88 s^-1) are performed to capture stress-strain responses across various conditions, with small-scale specimens enhancing fracture strain measurement accuracy, and quantify the Taylor-Quinney factor of the PEEK material during the adiabatic heating process. The findings demonstrate that the proposed constitutive model effectively predicts yield points across different strain rates and temperatures, with parameters easily obtainable through simple experimental methods, enhancing its practical applications.

Key words: constitutive model, viscoelastic-plastic, poly-ether-ether-ketone (PEEK), uniaxial tension, split Hopkinson pressure bar (SHPB)

中图分类号:

O345

. [J]. Applied Mathematics and Mechanics (English Edition), 2026, 47(3): 599-622.

Feiyang ZHAO, Jinzhao HUANG, Shangyang YU, Jikai YU, Licheng GUO. A novel dual-hardening viscoelastic-plastic constitutive model for thermoplastic resins[J]. Applied Mathematics and Mechanics (English Edition), 2026, 47(3): 599-622.

图/表 24

Property	Test standard	Unit	Value
Density	ISO 1138	g/cm³	1.3
Melting point	DSC	°C	343
Distortion temperature	ISO 75-1/-2	°C	163
Thermal expansion	ASTM D696	1/°C	$4.7 × 10 − 5$
Poisson’s ratio	ISO 572-2		0.4

$u ˙ / (mm ⋅ min − 1)$	1	20	100
$ε ˙ / s − 1$	0.002 29	0.030 64	0.193 61

Temperature/°C	Compressive relaxation				Tensile relaxation
Temperature/°C	$E 0$ /MPa	$E ¯ ∞$ /MPa	$η E$	$R fit 2$	$E 0$ /MPa	$E ¯ ∞$ /MPa	$η E$	$R fit 2$
23	3 389.21	2 991.66	$4 445.85 × 103$	0.67	3 299.54	3 053.63	$14 328.50 × 103$	0.94
100	2 897.90	2 519.62	$1 492.32 × 103$	0.31	2 856.40	2 587.80	$8 395.66 × 103$	0.97
140	2 634.26	2 359.99	$820.03 × 103$	0.39	2 402.26	2 124.45	$3 932.41 × 103$	0.90
180	1 102.80	598.93	$50.87 × 103$	0.36	988.80	383.32	$290.26 × 103$	0.96

Test	Relaxation parameter	$T < T g$		$T > T g$		$R fit 2$
Test	Relaxation parameter	Intercept	Slope	Intercept	Slope	$R fit 2$
C	E₀	$3.502 52 × 103$	$− 7.41$	$1.481 235 × 104$	$− 76.79$	0.965
C	$E ¯ ∞$	$3.262 57 × 103$	$− 7.68$	$1.760 157 × 104$	$− 95.65$	0.968
T	E₀	$3.598 61 × 103$	$− 6.44$	$1.577 411 × 104$	$− 81.50$	0.999
T	$E ¯ ∞$	$3.105 66 × 103$	$− 5.79$	$1.765 351 × 104$	$− 94.74$	0.990
C	$η E$	$4.816 00 × 106$	$− 28 117.95$	$4.816 000 × 106$	$− 28 117.95$	0.961
T	$η E$	$1.670 00 × 107$	$− 90 033.24$	$1.670 000 × 107$	$− 90 033.24$	0.994

JC property for tension
Parameter	$A T$	$C T$	$m T$	$B T$	n
Value	95.49	0.056 2	0.784 6	17.85	0.193 1
JC property for compression
Parameter	$A C$	$C C$	$m C$	$B 1 C$	$B 2 C$	$B 3 C$
Value	107.55	0.047 7	1.364 7	1 255.02	$− 8 630.37$	29 306.53
Strain rate and temperature property
Parameter	$ε ¯ 0$ /s^-1	$θ r / ∘ C$	$θ m / ∘ C$	$β int$	$C ν / (mJ ⋅ t − 1 ⋅ ° C -1)$
Value	0.002 29	23	343	0.48	$1.33 × 109$ ^[40]

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Strain rate/s^-1	Temperature/°C
Strain rate/s^-1	23	100	140	180
	Yield strength for tension/MPa
0.002 29	94.93	71.78	54.37	39.57
0.030 64	107.34	83.12	67.35	41.65
0.193 61	120.42	94.61	80.40	43.43
	Yield strength for compression/MPa
0.002 29	107.55	93.19	82.63	67.19
0.030 64	112.38	97.20	86.02	68.56
0.193 61	123.12	102.98	90.75	68.84

Strain rate/s^-1	1 094.08	2 859.31	4 018.49	5 641.70	5 957.88
Yield strength/MPa	202.90	208.77	213.61	217.28	219.41

Strain rate/s^-1	Simulation/MPa	Experiment/MPa	Deviation/%
1 094.08	197.96	202.90	2.43
2 859.31	205.69	208.77	1.47
4 018.49	208.45	213.61	2.41
5 641.70	211.60	217.28	2.61
5 957.88	212.18	219.41	3.29