text: Inside a magnet the wires are subjected to high Lorentz forces as well as thermal stresses during cooling. Any strain in the niobium tin causes a decrease in the superconducting performance of the material, and can cause the brittle material to fracture. Because of this, the wires need to be as stiff as possible. The Young's modulus of niobium tin is around 140 GPa at room temperature. However, the stiffness drops down to as low as 50 GPa when the material is cooled below . Engineers must therefore find ways of improving the strength of the material. Strengthening fibers are often incorporated in the composite niobium tin wires to increase their stiffness. Common strengthening materials include Inconel, stainless steel, molybdenum, and tantalum because of their high stiffness at cryogenic temperatures. Since the thermal expansion coefficients of the matrix, fiber, and niobium tin are all different, significant amounts of strain can be generated after the wire is annealed and cooled all the way down to operating temperatures. This strain is referred to as the pre-strain in the wire. Since any strain in the niobium tin generally decreases the superconducting performance of the material, a proper combination of materials must be used to minimize this value. The pre-strain in a composite wire can be calculated by the formula
  where ε is the pre-strain, ΔL/L and ΔL/L are changes in length due to thermal expansion of the niobium tin conduit and strengthening fiber respectively; V, V, V, and V are the volume fractions of conduit, fiber, copper, and bronze; σ, and σ are the yield stresses of copper and bronze; and E, and E are the Young's modulus of the conduit and the fiber. Since the copper and bronze matrix deforms plastically during cooldown, they apply a constant stress equal to their yield stress. The conduit and fiber, however, deform elastically by design. Commercial superconductors manufactured by the bronze process generally have a pre-strain value around 0.2% to 0.4%. The so-called strain effect causes a reduction in the superconducting properties of many materials including niobium tin. The critical strain, the maximum allowable strain over which superconductivity is lost, is given by the formula
  where ε is the critical strain, ε is a material dependent parameter equal to 1.5% in tension (−1.8% in compression) for niobium tin, B is the applied magnetic field, and B is the maximum upper critical field of the material. Strain in the niobium tin causes tetragonal distortions in the crystal lattice, which changes the electron-phonon interaction spectrum. This is equivalent to an increase in disorder in the A15 crystal structure. At high enough strain, around 1%, the niobium tin conduit will develop fractures and the current carrying capability of the wire will be irreversibly damaged. In most circumstances, except for high field conditions, the niobium tin conduit will fracture before the critical strain is reached.