Strengthening, crack arrest and multiple cracking in brittle materials using residual stresses

A method for processing a material, comprising:

• determining an apparent fracture toughness of the material over a range of crack sizes;
• wherein a change in the apparent fracture toughness with a change in the crack size is greater than a change in a stress intensity factor of the crack with the change in crack size;
• and
• introducing a compressive residual stress into the material based on the apparent fracture toughness over the range of crack sizes;
• wherein the absolute value of the compressive residual stress increases from a first value at a surface of the material to a second value within a depth in the material, the first value being smaller than the second value;
• and
• wherein the material will display multiple cracking and crack arrest without failure of the material when subjected to an applied stress that is less than an ultimate tensile strength of the material.

A method for introducing residual stress into a sodium silicate glass, comprising:

• performing a first ion exchange exchanging potassium ions for sodium ions to a first depth;
• performing a second ion exchange exchanging sodium ions for potassium ions to a second depth;
• wherein said first depth is greater than said second depth;
• and
• wherein the second ion exchange is carried out in a salt melt including a potassium to sodium molar ratio of greater than 1.