The Kröner solution is used to determine the shear modulus of any polycrystalline aggregate composed of cubic crystals. This solution from the self-consistent method takes the form of a cubic equation specified by the three elastic properties of the crystal. The ductile/brittle transition for homogeneous and isotropic materials in uniaxial tension is specified by terms of the shear modulus and the bulk modulus of the aggregate. These two basic results are then combined to specify the ductile/brittle transition of the polycrystalline aggregate in terms of its cubic crystal symmetry elastic properties. The various forms that the combined results take are developed and interpreted. Examples and detailed results are given for carbon-diamond, copper, tungsten, iron, silicon, lithium and platinum element type polycrystal materials. The tungsten and iron cases very closely bracket the ductile/brittle transition for all of the solids forming elements of the Periodic Table, one from the brittle side and the other from the ductile side.

Kröner解决方案用于确定由立方晶体组成的任何多晶聚集体的剪切模量。来自自洽方法的解决方案采用由晶体的三个弹性特性指定的三次方程式的形式。均质和各向同性材料在单轴拉伸中的延性/脆性转变是通过骨料的剪切模量和体积模量来指定的。然后将这两个基本结果组合起来，以根据其立方晶体对称弹性特性指定多晶聚集体的延性/脆性转变。合并结果采用的各种形式都得到开发和解释。给出了碳金刚石，铜，钨，铁，硅，锂和铂元素类型的多晶材料的实例和详细结果。