The tensile strength of a powder is related to the interparticle force and to the free volume, which, in turn, are related to consolidation stress. The relationship between stress and free volume is described by the state diagram that has been measured at zero shear for a set of cohesive powders (xerographic toners) with a range of concentrations of a flow control additive. The toners are 12.7 mu m diameter particles of styrene/butadiene copolymer, and the surface additive is a submicron fumed silica that is used to control the interparticle forces. To overcome problems of sample non-uniformity, powder samples are initially fluidized and then allowed to settle under gravity. The tensile strengths, sigma(t), of these powders have been measured by means of a powder bed technique in which gas flow through the bed is increased until the bed fractures due to the tensile stress produced by the gas flow. The overpressure required to fracture the bed then provides a measure of sigma(t). The consolidation stress in the bed, sigma(c), can be altered by varying the weight of the powder per unit area. Tensile strength is found to be linearly related to the consolidation stress in the limited range of stresses we have investigated, and the slope of this relationship is the same for all additive concentrations below 0.1%; above this concentration the slope decreases, consistent with a change from polymer-dominated to silica-dominated contacts between the particles. From the ratio sigma(t)/sigma(c), we show that the contacts are fully plastic even at zero load, and that hardness of the contacts increases with increasing additive concentration.