The critical-current density J(c) of an yttrium-barium-copper-oxide (YBCO) coated conductor deposited on a biaxially-textured Ni-5at.%W substrate was measured at 76.5 K as a function of axial tensile strain epsilon and magnetic field B applied parallel to the YBCO (a, b) plane. Reversibility of J(c), with strain was observed up to epsilon similar or equal to 0.6% over the entire field range studied (from 0.05 to 16.5 T), which confirms the existence of an intrinsic strain effect in YBCO coated conductors. J(c) vs. E depends strongly on magnetic field. The decrease of J(c) (epsilon) grows systematically with magnetic field above 2-3 T, and, unexpectedly, the reverse happens below 2 T as this decrease shrinks with increasing field. The pinning force density F-p = J(c) X B scaled with field for all values of strain applied, which shows that Fp can be written as K(T, epsilon)b(P)(1 - b)(q), where p and q are constants, K is a function of temperature and strain, b = B/B-c2* is the reduced magnetic field, and B* is the effective upper critical field at which Fp(B) extrapolates to zero.