ADHESION OF SPHERES - THE JKR-DMT TRANSITION USING A DUGDALE MODEL
ADHESION OF SPHERES - THE JKR-DMT TRANSITION USING A DUGDALE MODEL
复制标题
DOI：
10.1016/0021-9797(92)90285-t
复制
发表时间：
1992-04-01
影响因子：
9.9
通讯作者：
MAUGIS, D
中科院分区：
文献类型：
--
作者：
MAUGIS, D
在Johnson-Kendall-Roberts（JKR）近似中，接触区域外的粘附力被忽略，接触边缘的弹性应力是无限大的，就像线弹性断裂力学一样。另一方面，在Derjaguin-Muller-Toporov（DMT）近似中，考虑了粘附力，但轮廓被假设为赫兹，好像粘附力不能使表面变形。为了避免基于特定相互作用模型（例如Lennard-Jones势）的自洽数值计算，我们使用了Dugdale模型，该模型允许解析解。在裂纹尖端的长度范围内，粘附力假定为一个常数值σO，即理论应力。这种作用在气隙（外部裂纹）中的内部载荷导致应力强度因子Km，由于外部载荷，该应力强度因子Km与应力强度因子KI相抵消。这种抵消抑制了应力奇异性，保证了应力的连续性，并固定了裂纹半径和裂纹张开位移δt。能量释放率G由J积分计算，平衡由G =w给出。因此，平衡曲线a（P）、a（δ）和P（σ）、固定载荷或固定夹具时的粘附力、剖面和应力分布可以作为单个参数λ的函数绘制。当λ从零增大到无穷大时，存在从DMT近似到JKR近似的连续过渡。进而导出了DMT近似的G值。它表明，它是不物理上一致的，有张应力的接触区域和没有粘附力的外部或没有张应力的接触区域和粘附力的外部。在JKR近似中，粘附力的分布被简化为奇异应力atr=a+。接触外的总吸引力为零，接触内应力的积分等于外加载荷P，负的外加载荷由弹性恢复力支撑。在DMT近似中，附着应力趋于零，与应力atr=a−具有连续性，但它们的积分是有限的，接触外的总吸引力为2πwR。在接触区，应力呈赫兹分布，其积分为P + 27πwR。负的外加载荷由触点外部的粘着力维持。
In the Johnson-Kendall-Roberts (JKR) approximation, adhesion forces outside the area of contact are neglected and elastic stresses at the edge of the contact are infinite, as in linear elastic fracture mechanics. On the other hand, in the Derjaguin-Muller-Toporov (DMT) approximation, the adhesion forces are taken into account, but the profile is assumed to be Hertzian, as if adhesion forces Could not deform the surfaces. To avoid self consistent numerical calculations based on a specific interaction model (Lennard-Jones potential for example) we have used a Dugdale model, which allows analytical solutions. The adhesion forces are assumed to have a constant valueσO, the theoretical stress, over a lengthdat the crack tip. This internal loading acting in the air gap (the external crack) leads to a stress intensity factorKm, which is cancelled with the stress intensity factorKIdue to the external loading. This cancellation suppresses the stress singularities, ensures the continuity of stresses, and fixes the radiuscand the crack opening displacementδt. The energy release rateGis computed by theJ-integral and the equilibrium is given byG=w. The equilibrium curvesa(P), a(δ), andP(σ), the adherence forces at fixed load or fixed grips, the profiles, and the stress distributions can therefore be drawn as a function of a single parameter λ. When λ increases from zero to infinity there is a continuous transition from the DMT approximation to the JKR approximation. Furthermore the value ofGfor the DMT approximation is derived. It is shown that it is not physically consistent to have tensile stresses in the area of contact and no adhesion forces outside or no tensile stresses in the area of contact and adhesion forces outside. In the JKR approximation the distribution of adhesion forces is reduced to a singular stress atr=a+. The total attraction force outside the contact being zero, the integral of stresses in the contact is equal to the applied loadPand negative applied loads are supported by the elastic restoring forces. In the DMT approximation the adhesion stresses tend toward zero to have a continuity with the stress atr=a−, but their integral is finite and the total attraction force outside the contact is 2πwR. In the area of contact the distribution of stresses is Hertzian, and their integral isP+ 27πwR. Negative applied loads are sustained by adhesion forces outside the contact.