While uncontrolled residual stresses are undesirable, some designs rely on them. In particular, brittle materials can be toughened by including compressive residual stress, as in the case for toughened glass and pre-stressed concrete. The predominant mechanism for failure in brittle materials is brittle fracture, which begins with initial crack formation. When an external tensile stress is applied to the material, the crack tips concentrate stress, increasing the local tensile stresses experienced at the crack tips to a greater extent than the average stress on the bulk material. This causes the initial crack to enlarge quickly (propagate) as the surrounding material is overwhelmed by the stress concentration, leading to fracture.