考虑表面弹塑性本构的闭孔纳米泡沫金属强度理论与模型校验

Metals riddled with distributive nanovoids exhibit distinguished properties including high surface-to-volume ratio, low density, high strength and stiffness, high energy and sound absorbance, as well as high resistance to impact, humidity and extreme temperature. Theses properties make nanoporous metals a promising candidate in a variety of industrial applications. In the literature, most relevant works have been dedicated to raveling the failure mechanism of nanoporous metals, by the means of molecular dynamics simulation of void growth and coalescence. Nonetheless, numerical simulations call for a rigorous strength theory. To this end, we here aim to propose a multiscale strength model for predicting the mechanical failure of nanoporous metals. This project is tentatively composed of two major components as follows. First, we will design an elastoplastic constitutive model for the thin layer of void surfaces. When integrated with the constitutive model that describes the mechanical response of the matrix, we will construct the energy dissipation function due to plastic deformation under the limit condition of plastic flow. Following the limit analysis, a macroscopic constitutive relation bridging macroscopic limit stress and plastic strain rate can be derived. At this point, we are able to access both the limit function and its geometric boundary in terms of the invariants of the macroscopic limit stress tensor. Second, the theoretical model will be subsequently validated and fitted by both molecular dynamics simulations with conventional strain loads and simple nanoindentation experiments. The primary investigator of the proposed project has been working on the theoretical modeling, numerical simulation, and experimental analysis of multiscale mechanical problems for nearly two decades. If succeeded, a multiscale strength theory featured with elastoplastic surface mechanics can be developed for nanoporous metals, such that the parametric dependence of limit stress on porosity, elastoplastic surface material constants, void size and shape, inhomogeneity and anisotropy due to void distribution, temperature, and pore pressure can be quantitatively analyzed.

闭孔纳米泡沫金属具有比表面积高、轻质高强、抗震吸能、耐热防潮、降噪等突出优点，具备巨大应用潜力。现有研究多试图通过孔洞生长和聚合过程的数值模拟来理解此类材料的强度失效机制，但缺乏严谨的理论支撑。为了解决这一问题，本项目致力于：（1）设计面向孔洞表面层的弹塑性本构关系，结合基体弹塑性本构来构造材料的塑性变形能量耗散函数，并通过塑性流动极限分析得出宏观极限应力与宏观塑性应变率关系，从而建立宏观极限函数和极限面；（2）基于理论模型，设计并执行常见应变载荷分子动力学数值模拟和简单纳米压痕实验，进行模型校验和参数拟合。申请人在多尺度力学的理论推演、数值模拟和材料力学实验方面具有近20年经验，如成功，能建立考虑表面弹塑性本构的闭孔纳米泡沫金属强度理论，实现极限应力对孔隙率、孔洞表面弹塑性本构常数、孔洞尺寸与形状、孔洞分布非均匀性和各向异性、温度和孔洞压力等因素依赖关系的参数研究。

虽然闭孔纳米泡沫金属材料在结构形态上与传统多孔金属材料类似，但它具有更小的孔隙结构和更高的比表面积。因此，闭孔纳米泡沫金属材料的物理性质和力学性能不同于宏观结构，尤其不应再忽视表面效应的重要影响，从原理上理解闭孔纳米泡沫金属材料乃至超材料的强度准则、本构关系和力学性能，具有重要意义。本项目以闭孔纳米泡沫金属材料为研究对象，以理论分析和有限元数值模拟为主要研究方法，系统研究了闭孔纳米泡沫金属材料的宏观强度准则、弹塑性本构关系和力学性能，重点探讨了表面力学模型、表面参数、边界条件、孔隙率、孔洞形状、孔洞分布和拓扑结构等因素对闭孔纳米泡沫金属材料强度准则、本构关系和力学性能的影响。经过四年的研究，取得了预期的研究成果。.（1）基于表面弹性理论，解析求解了球状代表性体元的等效体积和剪切模量，建立了闭孔纳米泡沫金属材料的强度准则和弹塑性本构关系；.（2）基于表面塑性理论，推导了塑性耗散功率与基体屈服、表面残余应力和拉伸应力以及弯矩的关系，建立了强度准则和弹塑性本构关系；.（3）以Gurson孔洞模型为基础，得到了微观基体的膨胀率、等效应变率和塑性耗散功率，建立了包含微、纳闭孔金属材料的强度准则和弹塑性本构关系；.（4）利用Eshelby夹杂理论，建立了闭孔纳米泡沫金属材料跨尺度强度准则和弹塑性本构关系，揭示了表面效应和孔隙率对屈服轨迹和应力应变关系的作用机理；.（5）开发了考虑孔洞表面效应的闭孔纳米泡沫金属材料有限元程序，计算得到了表面效应参数、孔洞形状、尺寸、分布形式和孔隙率对局部应力集中和宏观力学性能的影响规律。.项目相关研究成果发表在Int. J. Eng. Sci.、Int. J. Mech. Sci.、Int. J. Solids Struct.、Mech. Mater.、Appl. Math. Model.、Compos. Struct.、Acta Mech.、Philos. Mag.、Math. Mech. Solids、Appl. Math. Comput.等力学、物理和数学领域的重要学术期刊上。项目的研究为闭孔纳米泡沫金属材料力学性能的研究提供了新思路，也对闭孔纳米泡沫金属材料和其他轻质高强结构材料的设计和制造具有重要指导价值。