Anomalous size effects in nanoporous materials induced by high surface energies
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Anomalous size effects in nanoporous materials induced by high surface energies Justin W. Wilkerson1,a) J. Mike Walker ’66 Department of Mechanical Engineering, Texas A&M University, College Station, Texas 77843, USA Address all correspondence to this author. e-mail: [email protected]
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Received: 13 January 2019; accepted: 21 February 2019
Several experiments and molecular dynamics calculations have reported anomalous mechanical behaviors of nanoporous materials that may be attributed to capillary effects. For example, nanoporous gold exhibits a tension–compression asymmetry in yield strength with the material being stronger in compression than tension. In addition, some molecular dynamics calculations have reported a spontaneous collapse of pores in nanoporous gold with nanometer-sized ligaments. Despite these perplexing observations, there are few theoretical models capable of shedding light on such capillary phenomena, particularly under general stress states. Here, we utilize a physics-based model to explore the implications of high surface energies on the mechanical response of dislocation-starved nanoporous materials subject to general stress states. For low stress triaxialities, we report an anomalous size effect and an anomalous temperature-dependence of dislocationstarved nanoporous materials with sufficiently large surface energies. Additionally, we provide an analytic criterion for spontaneous pore collapse in nanoporous materials with nanometer-sized ligaments.
Introduction and background The mechanical behavior of nanoporous materials has been studied extensively over the past two decades; see for example the earliest experiments on nanoporous gold [1, 2, 3]. Typically, the microstructure of nanoporous materials is characterized by two scalar quantities: the ligament size, denoted as k here, and the relative density of the porous material, denoted as q*. The strength of nanoporous materials is highly sensitive to both of these microstructural features. Typically, the Gibson–Ashby relations for foams are invoked to capture the softening of the yield strength ry with decreasing relative density (increasing porosity), i.e., ry } (q*)n, with n ; 3/2 being a rough fit for most materials [4]. For foams with ligaments tens of microns and larger in diameter, the yield strength is fairly insensitive to ligament size. However, for nanoporous materials, the ligaments are submicrons in diameter and exhibit size-dependent strengthening similar to nanowires and micropillars [5, 6, 7] This size-dependent strengthening of the ligament may be approximated by a power-law relationship, i.e., ry } km, [8, 9]. Typical values of the power-law exponent for nanoporous gold are m ; 0.3–0.7 [3, 10, 11, 12, 13, 14]. That said, these
ª Materials Research Society 2019
power-law relationships and (to some degree) more sophisticated scaling laws, e.g., [3, 15, 16, 17, 18], lack a satisfactory description of the underlying physics. In addition, these traditional relationships are developed for uniaxial stress conditions and
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