计入受压宽度的圆盘劈裂问题弹性解及应用

为了完善计入受压宽度的圆盘劈裂问题的理论基础，构建了一个可满足圆盘外表面任意应力条件的Airy应力函数，应用该应力函数推演了圆盘上、下外表面局部荷载作用下的弹性解，通过调整局部荷载的分布形态得到了与圆盘同半径刚性弧形垫条及承载压板下的圆盘劈裂问题解。研究了2种加载形式、荷载接触宽度、材料泊松比及不同平面假设条件下圆盘的应力-应变规律，提出了圆盘最大拉应力和最大拉应变的回归公式，讨论了圆柱体劈裂问题的应用。结果表明：圆盘的最大拉应力始终出现在圆心位置，其值随着荷载接触角的增加而减小，与套用集中力作用下圆盘劈裂强度计算式得到的劈裂强度偏差随着荷载接触角的加大而增大；圆盘的最大拉应变随着材料泊松比增大、荷载接触角缩小而加大，其位置也随之由圆心向荷载作用区靠近，且平面应变状态的最大拉应变比平面应力状态的最大拉应变大一些；在外荷载总量相同的情况下，平面应力状态的圆盘上、下对称轴的压缩量较平面应变状态的大一些，当材料泊松比分别为0.2，0.4时，两者相差约4%和20%；最后，给出了圆柱体劈裂强度及劈裂压缩强度比的计算式，并认为现行国际岩石力学学会（ISRM）、美国材料与试验协会（ASTM）和中国圆柱体劈裂试验规程中采用固定荷载半接触角为0.128的弧形垫条是必要且较适合的。

Elastic Solution of Disc-splitting Problem Considering Pressure Width and Its Application

In order to improve the theoretical basis of the disc-splitting problem considering pressure width, an Airy stress function that can satisfy the arbitrary stress condition of the external surface of the disc was established. This function was used to deduce the elastic solution of the disc under the local load of the upper and lower outer surfaces. By adjusting the distribution pattern of the local load, the disc-splitting problem under pressure through curved metallic strips with the same radius as the disc or the rigid platen was obtained. The stress-strain law of the disc under two kinds of loading, different contact widths, Poisson's ratio, and plane assumptions was studied. The regression formula of the maximum tensile stress (strain) was proposed, and the application of the disc-splitting problem was also discussed. The results show that the maximum tensile stress of the disc always appears at the center of the disc, and it decreases with increasing contact angle. The deviation between the disc-splitting strength obtained in this study and the splitting strength calculated using the disc-splitting strength formula under concentrated force increased with increasing load contact angle. With the increase in Poisson's ratio or the decrease in contact angle, the maximum tensile strain increases, and its location gradually moves from the center to the load zone. The maximum tensile strain in the plane strain state is larger than that in the plane stress state. Under the same external load, the compression value of the upper and lower symmetry axes of the disc in the plane stress state is larger than that in the plane strain state. When the Poisson's ratio is 0.2 and 0.4, respectively, the difference between the two is approximately 4% and 20%. Finally, the formula for determining the splitting strength of the cylinder and the splitting compression strength ratio is given. It is suitable for the International Society of Rock Mechanics, American Society of Materials and Testing and Chinese Industry Standard recommend the adoption of curved strips with fixed half contact angle of 0.128 for the cylinder-splitting test.