Dynamical Mechanical Thermal Analysis of Shape-Memory Polymers

Abstract

This chapter is dedicated to the dynamical mechanical thermal analysis of shape-memory polymers. Temperature obviously plays a major role in the mechanical properties of these materials; hence, the understanding of the physical phenomena driving the shape-memory effect is of first importance for the design of practical applications in which shape-memory polymers are used. The shape-memory effect being closely related to the viscoelastic behavior of the polymer, it is important to properly describe it with appropriate tools. The objective of this chapter is to describe characterization methods, models, and parameters identification techniques that can be easily used for the description of the thermomechanical behavior of SMPs. The associated models can easily be implemented in finite element codes for time- or frequency-domain simulations. The experimental results and all numerical values of the models are provided for three shape-memory polymers: the tBA/PEGDMA and a vitrimer, which can easily be manufactured according to the data provided in open literature, and a shape-memory polymer filament for 3D printing, which is available on the shelf.

Appendices

Appendix - Numerical Values of the GMM for the Master Curve of tBA/PEGDMA

Cell Id (i)	$\infty$	1	2	3	4	5
$\tau _i$ [s$^{-1}$]	0	$6.3559\times 10^{-8}$	$1.0593\times 10^{-7}$	$3.1780\times 10^{-7}$	$7.2089\times 10^{-7}$	$1.6353\times 10^{-6}$
$E_i$ [MPa]	0.97769	47.494	12.824	36.857	25.597	38.480
6	7	8	9	10	11	12
$3.7094\times 10^{-6}$	$8.4144\times 10^{-6}$	$1.9087\times 10^{-5}$	$4.3297\times 10^{-5}$	$9.8215\times 10^{-5}$	0.00022279	0.00050538
35.509	44.348	45.331	51.465	54.857	60.001	63.611
13	14	15	16	17	18	19
0.0011464	0.0026005	0.0058989	0.013381	0.030354	0.068854	0.15619
68.674	72.789	77.466	82.927	90.182	100.64	117.60
20	21	22	23	24	25	26
0.35430	0.80368	1.8231	4.1354	9.3808	21.279	48.270
147.41	195.49	236.00	181.53	88.156	38.936	17.638
27	28	29	30	31	32	33
109.50	248.38	563.42	1278.1	3149.0	7758.6	19116
8.4675	4.2157	2.0917	1.1444	0.59268	0.28032	0.13926
34	35	36	37	38	39	40
47100	$1.1605\times 10^{5}$	$2.8593\times 10^{5}$	$7.0448\times 10^{5}$	$1.7357\times 10^{6}$	$4.2766\times 10^{6}$	$1.2830\times 10^{7}$
0.067803	0.032689	0.017485	0.0050210	0.0028528	0.0049602	0.013080
41
$2.1383\times 10^{7}$
0.021141

Appendix - Numerical Values of the GMM for the Master Curve of SMP Filament

Cell Id (i)	$\infty$	1	2	3	4	5
$\tau _i$ [s$^{-1}$]	0	$1.3656\times 10^{-10}$	$6.8280\times 10^{-10}$	$1.5076\times 10^{-9}$	$3.3288\times 10^{-9}$	$7.3499\times 10^{-9}$
$E_i$ [MPa]	0.00041175	122.25	27.421	46.242	31.513	57.238
6	7	8	9	10	11	12
$1.6228\times 10^{-8}$	$3.5832\times 10^{-8}$	$7.9117\times 10^{-8}$	$1.7469\times 10^{-7}$	$3.8571\times 10^{-7}$	$8.5164\times 10^{-7}$	$1.8804\times 10^{-6}$
46.875	62.971	58.318	66.349	68.579	73.597	81.764
13	14	15	16	17	18	19
$4.1519\times 10^{-6}$	$9.1673\times 10^{-6}$	$2.0241\times 10^{-5}$	$4.4693\times 10^{-5}$	$9.8681\times 10^{-5}$	0.00021789	0.00048109
91.310	100.64	121.28	127.62	153.02	151.15	152.60
20	21	22	23	24	25	26
0.0010622	0.0023454	0.0051786	0.011434	0.025247	0.055744	0.12308
123.22	90.911	58.486	35.484	20.420	11.493	6.0686
27	28	29	30	31	32	33
0.27176	0.60005	1.3249	2.9254	6.4592	14.262	31.490
3.2138	1.3316	0.87233	0.46338	0.63790	0.32339	0.65854
34	35	36	37	38	39	40
69.529	153.52	338.97	748.43	1652.5	3648.8	18244
0.24972	0.86167	0.87394	0.00047364	2.6729	0.66321	0.00059484

Appendix - Numerical Values of the GMM for the Master Curve of Vitrimer

Cell Id (i)	$\infty$	1	2	3	4	5
$\tau _i$ [s$^{-1}$]	0	0.012689	0.063445	0.14123	0.31438	0.69983
$E_i$ [MPa]	10.806	1517.2	9.9502	790.00	0.049548	500.70
6	7	8	9	10	11	12
1.5579	3.4678	7.7195	17.184	38.252	85.151	189.55
203.33	345.30	251.11	289.77	249.72	254.53	229.18
13	14	15	16	17	18	19
421.94	939.26	2090.8	4654.3	10361.	23063.	51339.
217.72	193.13	171.00	142.87	115.73	88.780	65.993
20	21	22	23	24	25	26
$1.1428\times 10^{5}$	$2.5440\times 10^{5}$	$5.6630\times 10^{5}$	$1.2606\times 10^{6}$	$2.8062\times 10^{6}$	$6.2466\times 10^{6}$	$1.3905\times 10^{7}$
47.155	33.193	22.616	15.297	9.7769	6.3134	3.8148
27	28	29	30	31	32	33
$3.0954\times 10^{7}$	$6.8904\times 10^{7}$	$1.5338\times 10^{8}$	$3.4144\times 10^{8}$	$7.6005\times 10^{8}$	$1.6919\times 10^{9}$	$3.7662\times 10^{9}$
2.6396	1.6391	1.3584	0.83093	0.87719	0.46957	0.69845
34	35	36	37	38
$8.3838\times 10^{9}$	$1.8663\times 10^{10}$	$4.1544\times 10^{10}$	$9.2478\times 10^{10}$	$4.6239\times 10^{11}$
0.41526	0.00059210	0.0012208	0.0050371	14.355