In Fracture Mechanics everyone I can find attributes the relationship between G and K to Irwin's 1957 paper. However he does not do so, he defines the Stress Intensity factor in terms of E and G. Does anyone know when/where he actually said G=Ksquared/E???
Are the G and K you mentioned in the 1st sentence the Energy Release Rate and Stress Intensity Factor? If so, then the definition of the Stress Intensity Factor (K) in terms of E and G IS the relation between G and K. If you compare his expressions for stresses (equations [10] and [11] of his paper in Journal of applied mechanics, 1957) and those found now in terms of stress intensity factors, as you said, he defined stress intensity factor in terms of E and G. Or later in his Conclusion or the paragraph above the Conclusion, he stated that (stress) intensity factor is the square root of (E G/pi). Except the constant pi which can be moved out the relation, this is the relation K= square root of (E G), or G= (square of K) / E.
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