Research on Constitutive Model of Low-temperature Concrete Subjected to Impact Load

doi:10.12382/bgxb.2023.1090

Abstract

Abstract:

The mechanical properties of concrete in a cold environment are different from those in normal temperature state. The impact loading test of concrete is made to study the dynamic mechanical properties of concrete under low temperature environment. In consideration of the influence of temperature and strain rate, the impact damage law of low-temperature concrete is analyzed by introducing the temperature effect based on damage theory of thermal activation energy. The moduli of all components of low-temperature concrete are associated with each other to obtain the equivalent modulus of concrete by using the principle of mixing law, the spherical model of two-phase material and the strain rate effect. Damage evolution function is introduced into Drucker-Prager yield criterion, which is established with temperature and strain rate as parameters, and a dynamic constitutive model of low temperature service concrete is proposed. The results show that the size of concrete fragments increases significantly and the damage situation decreases with the decrease in service temperature, which shows that the free water condenses into ice in concrete pore cracks at low temperature, and ice has a certain bonding effect on pore cracks. With the decrease in temperature, this bonding effect is strengthened, thus inhibiting the development of damage during impact loading. With the decrease in service temperature, the content and modulus of ice in pores increase, and the strength of concrete is significantly enhanced.

Key words: concrete, low temperature service, damage, moisture content, constitutive model

CLC Number:

O347

NING Jianguo, LI Yuhui, YANG Shuai, XU Xiangzhao. Research on Constitutive Model of Low-temperature Concrete Subjected to Impact Load[J]. Acta Armamentarii, 2024, 45(12): 4339-4349.

Figures/Tables 17

Fig.1 Size distribution and local magnification of fragments at different temperatures after impact of 200s-1

Fig.2 Schematic diagram of microcrack growth under impact state

Table 1 Temperature-dependent damage correction factors

温度/℃	20	-10	-20	-30
K_T	1.67×10^-5	1.50×10^-5	1.45×10^-5	1.39×10^-5

Table 2 Segmented damage parameters

参数	应变率/s^-1
参数	100	200	300
b	2.92	2.81	2.49
c₁	0.85	0.70	0.68
c₂	0.62	0.54	0.60

Table 3 Modulus of ice at low temperatures

模量	温度/℃
模量	20	-10	-20	-30
K_i/GPa		5.793	6.423	7.083
G_i/GPa		2.655	2.955	3.255

Table 4 Related parameters of concrete modulus

参数	数值	参数	数值
φ_s	0.84	ω	0.04
φ_w0	0.04	θ	-0.203
K_s/GPa	26.071	ρ_i/(g·cm^-3)	0.917
G_s/GPa	11.820	ρ_w/(g·cm^-3)	1.000
K_w/GPa	2.250	λ₁	-0.083
G_w/GPa	0.000	λ₂	0.027

Table 5 Equivalent modulus E ¯ d of concrete at different temperatures and strain ratesGPa

$ε ·$ /s^-1	温度/℃
$ε ·$ /s^-1	20	-10	-20	-30
100	28.669	24.356	24.112	24.897
200	32.167	28.507	28.245	28.750
300	39.887	34.122	33.965	34.857

Table 5 Equivalent modulus E ¯ d of concrete at different temperatures and strain ratesGPa

$ε ·$ /s^-1	温度/℃
$ε ·$ /s^-1	20	-10	-20	-30
100	28.669	24.356	24.112	24.897
200	32.167	28.507	28.245	28.750
300	39.887	34.122	33.965	34.857

Table 6 Initial damage of concrete at different temperatures

温度/℃	20	-10	-20	-30
D₀	0.2480	0.2455	0.2455	0.2458

Fig.3 Concrete sample (part)

Fig.4 SHPB device

Fig.5 Voltage-timecurves and stress balance check

Table 7 Basic parameters of concrete under different curing temperatures and strain rates

试验工况	σ_s0/MPa	ε_m	σ_m/MPa
T20S100	20.134	0.0079	28.037
T20S200	32.017	0.0049	35.453
T20S300	37.542	0.0046	42.464
T-10S100	24.016	0.0048	30.531
T-10S200	32.451	0.0027	37.417
T-10S300	39.462	0.0030	44.368
T-20S100	27.958	0.0042	34.442
T-20S200	39.534	0.0031	45.170
T-20S300	48.696	0.0037	53.587
T-30S100	32.469	0.0048	38.621
T-30S200	38.738	0.0029	45.136
T-30S300	52.541	0.0022	59.729

Table 8 Plasticity parameters of constitutive model

应变率/s^-1	n_p	ξ	h	n_q
100	1.7	2.044×10^-4	2.96×10²	1.6
200	1.5	1.870×10^-4	2.95×10²	1.6
300	1.4	1.421×10^-4	2.85×10²	1.6

Fig.6 Stress-strain curves at different strain rates at 20℃

Fig.7 Stress-strain curves at different strain rates at -10℃

Fig.8 Stress-strain curves at different strain rates at -20℃

Fig.9 Stress-strain curves at different strain rates at -30℃

References 46

[1]	THAKUR I C. Properties of concrete incorporated with ggbs[J]. International Journal of Research in Engineering and Technology, 2016, 5:275-281.
[2]	吕映庆, 陈南勋, 武海军, 等. 弹体高速侵彻超高性能混凝土靶机理[J]. 兵工学报, 2022, 43(1):37-47. doi: 10.3969/j.issn.1000-1093.2022.01.005
	LÜ Y Q, CHEN N X, WU H J, et al. Mechanism of high-velocity projectile penetrating into ultra-high performance concrete target[J]. Acta Armamentarii, 2022, 43(1):37-47. (in Chinese) doi: 10.3969/j.issn.1000-1093.2022.01.005
[3]	VERSTRYNGE E, LACIDOGNA G, ACCORNERO F, et al. A review on acoustic emission monitoring for damage detection in masonry structures[J]. Construction and Building Materials, 2021, 268:121089.
[4]	SUARIS W, SHAH S P. Constitutive model for dynamic loading of concrete[J]. Journal of Structural Engineering, 1985, 111(3):563-576.
[5]	RIEDEL W, THOMA K, HIERMAIER S, et al. Penetration of reinforced concrete by BETA-B-500 numerical analysis using a new macroscopic concrete model for hydrocodes[C]// Proceedings of the 9th International Symposium. Berlin, Germany: Interaction of the Effects of Munitions with Structures, 1999:1-8.
[6]	QIAO Y, WANG H F, CAI L C, et al. Influence of low temperature on dynamic behavior of concrete[J]. Construction and Building Materials, 2016, 115:214-220.
[7]	MACLEAN T J, LLOYD A. Compressive stress-strain response of concrete exposed to low temperatures[J]. Journal of Cold Regions Engineering, 2019, 33(4):4019014.
[8]	KOGBARA R B, IYENGAR S R, GRASLEY Z C, et al. A review of concrete properties at cryogenic temperatures:towards direct LNG containment[J]. Construction and Building Materials, 2013, 47:760-770.
[9]	宁建国, 杨帅, 李玉辉, 等. 低温/常温养护下混凝土的本构模型和抗爆试验研究[J]. 兵工学报, 2023, 44(10):2932-2943. doi: 10.12382/bgxb.2022.1019
	NING J G, YANG S, LI Y H, et al. Research on constitutive model and blast resistance test of concrete under low/normal temperature curing[J]. Acta Armamentarii, 2023, 44(10):2932-2943. (in Chinese)
[10]	ZHOU J K, DING N. Moisture effect on compressive behavior of concrete under dynamic loading[J]. Journal of Central South University, 2014, 21(12):4714-4722.
[11]	MIURA T. The properties of concrete at very low temperatures[J]. Materials and Structures, 1989, 22(4):243-254.
[12]	HU S W, FAN B. Crack extension resistance of concrete under low temperatures[J]. Magazine of Concrete Research, 2020, 72(15/16):837-851.
[13]	JIANG Z W, DENG Z L, ZHU X P, et al. Increased strength and related mechanisms for mortars at cryogenic temperatures[J]. Cryogenics, 2018, 94:5-13.
[14]	时旭东, 汪文强, 田佳伦. 不同强度等级混凝土遭受超低温冻融循环作用的受压强度试验研究[J]. 工程力学, 2020, 37(2):211-220.
	SHI X D, WANG W Q, TIAN J L. Experimental study on the compressivestrength of concrete of different strength grades experiencing ultralow temperature freeze-thaw cycle action[J]. Engineering Mechanics, 2020, 37(2):211-220. (in Chinese)
[15]	CAI Y Q, ZHANG Y, LIU Y, et al. Predictive method for the macroscopic mechanical properties of concrete at ultra-low temperatures[J]. Construction and Building Materials, 2022, 357:129276.
[16]	SHEN Y J, LÜ Y, YANG H W, et al. Effect of different ice contents on heat transfer and mechanical properties of concrete[J]. Cold Regions Science and Technology, 2022, 199:103570.
[17]	刘锋, 李庆明. 混凝土类材料动态压缩强度在多维应力状态下的应变率效应[J]. 爆炸与冲击, 2022, 42(9):123-138.
	LIU F, LI Q M. Stain-rate effects on the dynamic compressive strength of concrete-like materials under multiple stress state[J]. Explosion and Shock Waves, 2020, 42(9):123-138. (in Chinese)
[18]	刘陆广, 欧卓成, 段卓平, 等. 混凝土动态断裂数值模拟研究[J]. 兵工学报, 2010, 31(6):741-745.
	LIU L G, OU Z C, DUAN Z P, et al. Simulation of concrete dynamic fracture[J]. Acta Armamentarii, 2010, 31(6):741-745. (in Chinese)
[19]	付应乾, 俞鑫炉, 董新龙, 等. 混凝土材料拉伸强度的应变率强化效应实验研究[J]. 兵工学报, 2020, 41(1):143-151. doi: 10.3969/j.issn.1000-1093.2020.01.017
	FU Y Q, YU X L, DONG X L, et al. An experimental investigation on the strain rate-dependent tensile strength of plain concretes[J]. Acta Armamentarii, 2020, 41(1):143-151. (in Chinese) doi: 10.3969/j.issn.1000-1093.2020.01.017
[20]	JIA B, TAO J L, LI Z L, et al. Effects of temperature and strain rate on dynamic properties of concrete[J]. Transactions of Tianjin University, 2008, 14(S1):511-513.
[21]	EIBL J, SCHMIDT-HURTIENNE B. Strain-rate-sensitive constitutive law for concrete[J]. Journal of Engineering Mechanics, 1999, 125(12):1411-1420.
[22]	CRAEYE B, GEIRNAERT M, SCHUTTER G D. Super absorbing polymers as an internal curing agent for mitigation of early-age cracking of high-performance concrete bridge decks[J]. Construction and Building Materials, 2011, 25(1):1-13.
[23]	GRADY D E, KIPP M E. Continuum modeling of explosive fracture in oil shale[J]. International Journal of Rock Mechanics & Mining Science & Geomechanics Abstracts, 1980, 17(3):147-157.
[24]	TAYLOR L M, CHEN E P, KUSZMAUL J S. Microcrack-induced damage accumulation in brittle rock under dynamic loading[J]. Computer Methods in Applied Mechanics & Engineering, 1986, 55(3):301-320.
[25]	LAMBERT D E, ROSS C A. Strain rate effects on dynamic fracture and strength[J]. International Journal of Impact Engineering, 2000, 24(10): 985-998.
[26]	TANDON S, FABER K T. Effects of loading rate on the fracture of cementitious materials[J]. Cement and Concrete Research, 1999, 29(3):397-406.
[27]	BUDIANSKY B, O’CONNELL R J. Elastic moduli of a cracked solid[J]. International Journal of Solids and Structures, 1976, 12(2):81-97.
[28]	宁建国, 商霖, 孙远翔. 混凝土材料冲击特性的研究[J]. 力学学报, 2006, 38(2):199-208. doi: 10.6052/0459-1879-2006-2-2005-172
	NING J G, SHANG L, SUN Y X. Research on impact characteristics of concrete materials[J]. Chinese Journal of Theoretical and Applied Mechanics, 2006, 38(2):199-208. (in Chinese)
[29]	王礼立, 蒋昭镳, 陈江瑛. 材料微损伤在高速变形过程中的演化及其对率型本构关系的影响[J]. 宁波大学学报(理工版), 1996, 9(3):47-55.
	WANG L L, JIANG Z B, CHEN J Y. Micro-damage evolution in high velocity deformation and its influence on rate-dependent constitutive relation of material[J]. Journal of Ningbo University (Natural Science & Engineering Edition), 1996, 9(3):47-55. (in Chinese)
[30]	ZHU Z W, JIA J X, ZHANG F L. A damage and elastic-viscoplastic constitutive model of frozen soil under uniaxial impact loading and its numerical implementation[J]. Cold Regions Science and Technology, 2020, 175:10381.
[31]	GLUCKLICH J. The effect of microcracking on time-dependent deformations and the long-term strength of concrete[R]. London, UK: Cement and Concrete Association, 1968:176-189.
[32]	FU T T, ZHU Z W, MA W, et al. Damage model of unsaturated frozen soil while considering the influence of temperature rise under impact loading[J]. Mechanics of Materials, 2021, 163:104073.
[33]	SUN Z H, SCHERER G W. Pore size and shape in mortar by thermoporometry[J]. Cement and Concrete Research, 2010, 40(5):740-751.
[34]	GONG F Y, JACOBSEN S, LI P F, et al. Modeling of path-dependent phase change in sorption and freezing of pore water for cementitious materials[J]. Journal of Building Engineering, 2022, 57:104969.
[35]	SUN Z H, SCHERER G W. Effect of air voids on salt scaling and internal freezing[J]. Cement and Concrete Research, 2010, 40:260-270.
[36]	ZHANG M Y, ZHANG X Y, LU J G, et al. Analysis of volumetric unfrozen water contents in freezing soils[J]. Experimental Heat Transfer, 2018, 32(5): 426-438.
[37]	ZHU Z W, LIU Z J, XIE Q J, et al. Dynamic mechanical experiments and microstructure constitutive model of frozen soil with different particle sizes[J]. International Journal of Damage Mechanics, 2018, 27(5):686-706.
[38]	徐敩祖, J.L. 奥利奋特, A.R. 泰斯. 土水势、未冻水含量和温度[J]. 冰川冻土, 1985, 7(1):1-14.
	XU X Z, OLIPHANT J L, TICE A R. Soil-water potential and unfrozen water content and temperature[J]. Journal of Glaciology and Geocryology, 1985, 7(1):1-14. (in Chinese)
[39]	CHANG D, LAI Y M, ZHANG M Y. A meso-macroscopic constitutive model of frozen saline sandy soil based on homogenization theory[J]. International Journal of Mechanical Sciences, 2019, 159:246-259.
[40]	MORI T, TANAKA K. Average stress in matrix and average elastic energy of materials with misfitting inclusions[J]. Acta Metallurgica, 1973, 21(5):571-574.
[41]	郑金城, 徐超, 彭刚, 等. 预静态加载后的混凝土动态受压特性试验[J]. 实验力学, 2013, 28(3):352-359.
	ZHENG J C, XU C, PENG G, et al. Experimental study on dynamic compressive behaviors of concrete due to monotonic loading history[J]. Journal of Experimental Mechanics, 2013, 28(3):352-359. (in Chinese)
[42]	LU Y, XU K. Modeling of dynamic behavior of concrete materials under blast loading[J]. International Journal of Solids and Structures, 2004, 41:131-143.
[43]	DRUCKER D C, PRAGER W. Soil mechanics and plastic analysis or limit design[J]. Quarterly of Applied Mathematics, 1952, 10(2):157-165.
[44]	LIU H R, DING T, XIAO J Z, et al. Buildability prediction of 3D-printed concrete at early-ages:a numerical study with Drucker-Prager model[J]. Additive Manufacturing, 2022, 55:102821.
[45]	ZHANG F L, ZHU Z W, MA W, et al. A unified viscoplastic model and strain rate-temperature equivalence of frozen soil under impact loading[J]. Journal of the Mechanics and Physics of Solids, 2021, 152(2):104413.
[46]	NING J G, LIU H F, SHANG L. Dynamic mechanical behavior and the constitutive model of concrete subjected to impact loadings[J]. Science in China, 2008, 51:1745-1760.