冲击载荷下煤体巴西劈裂动态力学特性及损伤本构模型

Dynamic mechanical properties and damage constitutive model of coal in Brazilian splitting under impact load

  • 摘要: 在深部煤层开采过程中,煤体在冲击载荷扰动下的动态损伤与破坏是造成重大动力灾害的关键因素。为探究冲击载荷下煤样的动态拉伸特性,采用霍普金森压杆(SHPB)试验系统,开展不同冲击速度下煤的动态劈裂拉伸试验,并利用高速摄像机拍摄煤样的裂纹扩展过程,研究不同冲击速度下煤样的动态拉伸力学特性,分析巴西劈裂试验中煤样的破坏过程及破坏形态。基于组合元件模型理论和统计损伤理论,构建了煤体动态损伤本构模型,并验证了模型的合理性。试验结果表明:煤样的峰值拉伸强度与冲击速度成正比关系,而峰值应变与冲击速度成反比,这表明随冲击速度的增加,煤样的变形反应时间较短,在小变形之后就发生宏观破裂。动态劈裂试验中,中心主裂纹在煤样中心区域产生,随后产生的微裂纹不断扩展、汇聚直至贯通,导致煤样破裂,在近杆件端面处产生应力集中现象,出现压碎区域。随冲击速度的增大,煤样所吸收的能量也随之增加,入射能、反射能、透射能及耗散能均呈现增大趋势。其中,入射能的增长斜率最大,透射能变化幅度较小,增长斜率最小,煤样耗散能与反射能增长斜率近似相等。煤样能量耗散密度随冲击速度增大呈线性增加,这表明随冲击速度的增大,高能量的输入导致能量在煤体内部迅速传递积累,局部区域承受更高的能量密度,使得煤样的破裂程度更加显著。基于朱−王−唐模型及统计损伤理论,将部分弹性体损伤化并引入塑性元件,对朱−王−唐本构模型进行改进,构建了冲击载荷下煤体巴西劈裂的黏弹塑性动态损伤本构模型。该模型能够较好地表征冲击载荷作用下煤体的弹性阶段及塑性阶段,很好地反映煤体在不同冲击速度下的动态应力−应变关系,验证了本构模型的可靠性。

     

    Abstract: In the process of deep coal seam mining, the dynamic damage and failure of coal under impact load disturbance are key factors triggering major dynamic disasters. To explore the dynamic tensile properties of coal samples under impact loads, the Split Hopkinson Pressure Bar (SHPB) test system was adopted to perform dynamic splitting tensile tests on coal samples under varying impact velocities, while a high-speed camera was utilized to record the crack initiation and propagation processes of the samples. The dynamic tensile mechanical properties of coal samples under varying impact velocities were systematically investigated, and the failure processes and modes of coal samples in the dynamic Brazilian splitting tests were analyzed in detail. Based on the combined element model theory and statistical damage theory, a dynamic damage constitutive model for coal was established, and its rationality was verified by means of experimental data. The test results indicated that the peak tensile strength of coal samples exhibited a positive proportional relationship with impact velocity, whereas the peak strain showed an inverse proportional relationship with impact velocity. This phenomenon implied that as the impact velocity increases, the deformation response time of coal samples is significantly shortened, and macroscopic fracture occurs with only minimal deformation. In the dynamic splitting tests, a central main crack initiated in the central region of coal samples, followed by the continuous propagation, coalescence, and eventual penetration of microcracks, ultimately resulting in the complete fracture of the samples. Notably, stress concentration occurred near the pressure bar end faces, accompanied by the formation of crushing zones. As impact velocity rose, the energy absorbed by coal samples similarly increased, and incident, reflected, transmitted, and dissipated energies all exhibited an upward trend. Among these, incident energy showed the steepest growth slope; transmitted energy had the smallest variation range and the gentlest growth slope; and the growth slopes of dissipated and reflected energies of coal samples were approximately equal. The energy dissipation density of coal samples increased linearly with increasing impact velocity. This demonstrates that as impact velocity increases, high energy input induces rapid energy transfer and accumulation in the coal matrix, with local regions sustaining higher energy densities, thereby enhancing the fracture degree of coal samples. Based on the Zhu-Wang-Tang model and statistical damage theory, damage characteristics of specific elastic components were incorporated into plastic elements. The Zhu-Wang-Tang constitutive model was then modified, and accordingly, a viscoelastic-elastoplastic dynamic damage constitutive model was established for coal subjected to Brazilian splitting under impact loads. This model effectively characterized the elastic and plastic stages of coal under impact loads and accurately reflected the dynamic stress-strain relationships of coal under different impact velocities, thus verifying the reliability of the constitutive model.

     

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