A method for forming a graphene-reinforced polymer matrix composite, comprising: (a) distributing graphite microparticles into a molten thermoplastic polymer phase consisting essentially of one or more molten thermoplastic polymers to form a graphite-molten thermoplastic polymer phase, wherein at least 50% of the graphite in the graphite microparticles consists of multilayer graphite crystals between 1.0 and 1000 microns thick along a c-axis direction; and (b) applying a succession of shear strain events to the graphite-molten thermoplastic polymer phase while imparting elongational flow so that shear stress within said molten polymer phase exceeds the Interlayer Shear Strength of said graphite microparticles and said molten polymer phase exfoliates the graphite microparticles successively with each event, until said graphite microparticles are at least partially exfoliated to form a distribution in the molten polymer phase of single- or multilayer graphene nanoparticles, or both, less than 10 nm thick in a c-axis direction, and further continuing the shear strain events until fracturing of said exfoliated single- or multilayer graphene sheets occurs across the basal plane and produces reactive free radical graphenic carbon bonding sites on the fractured edges of said single- or multilayer graphene sheets that react with said one or more molten thermoplastic polymers to provide a composite where thermoplastic polymer chains are directly covalently bonded to, and inter-molecularly cross-linked by, said single- or multilayer graphene sheets; wherein the succession of shear strain events which provides the composite where thermoplastic polymer chains are directly covalently bonded to, and inter-molecularly cross-linked by, said single- or multilayer graphene sheets, is a series of at least 1,000 to over 10,000,000 alternating pulses of a first, shear strain rate and a second, shear strain rate, wherein the first shear strain rate is between 100 and 10,000 sec -1 and is at least twice the magnitude of the second strain rate. (a) distributing graphite microparticles into a molten thermoplastic polymer phase consisting essentially of one or more molten thermoplastic polymers to form a graphite-molten thermoplastic polymer phase, wherein at least 50% of the graphite in the graphite microparticles consists of multilayer graphite crystals between 1.0 and 1000 microns thick along a c-axis direction; and (b) applying a succession of shear strain events to the graphite-molten thermoplastic polymer phase while imparting elongational flow so that shear stress within said molten polymer phase exceeds the Interlayer Shear Strength of said graphite microparticles and said molten polymer phase exfoliates the graphite microparticles successively with each event, until said graphite microparticles are at least partially exfoliated to form a distribution in the molten polymer phase of single- or multilayer graphene nanoparticles, or both, less than 10 nm thick in a c-axis direction, and further continuing the shear strain events until fracturing of said exfoliated single- or multilayer graphene sheets occurs across the basal plane and produces reactive free radical graphenic carbon bonding sites on the fractured edges of said single- or multilayer graphene sheets that react with said one or more molten thermoplastic polymers to provide a composite where thermoplastic polymer chains are directly covalently bonded to, and inter-molecularly cross-linked by, said single- or multilayer graphene sheets; wherein the succession of shear strain events which provides the composite where thermoplastic polymer chains are directly covalently bonded to, and inter-molecularly cross-linked by, said single- or multilayer graphene sheets, is a series of at least 1,000 to over 10,000,000 alternating pulses of a first, shear strain rate and a second, shear strain rate, wherein the first shear strain rate is between 100 and 10,000 sec -1 and is at least twice the magnitude of the second strain rate.