We have measured the tensile strength and average free volume of fine cohesive powders as a function of consolidation stress in the range of low consolidation stresses. All the measurements start by fluidizing the powder. Once the powder is homogeneously fluidized, the fluidizing gas is reduced to a value below the minimum fluidization flow. In this way, the powder bed settles down under a consolidation stress below its weight per unit area. The average free volume is calculated by measuring the powder bed height by means of an ultrasonic sensor. Then the gas flow is slowly increased until the powder breaks, enabling us to measure the powder tensile strength. This process is repeated for different values of the decompressing gas flow. We show that at low consolidations, there exists a linear relationship between the tensile strength and the consolidation stress. From the measured consolidation stress. tensile strength and average free volume, we estimate the interparticle consolidation force per contact, F-c and the interparticle tensile force per contact, F-t. We show that F-t increases linearly with F-c and is independent of particle size. This result implies that, at low consolidations, the contact between fine cohesive particles is plastic.