From a design point of view, tires belong to that class of structures known as laminated fiber-reinforced composites. Other examples of such structures include rocket motor cases, aircraft parts and tennis rackets – but these entities tend to behave elastically while undergoing small deformations with geometries well suited to standard textbook calculations. Consider that the PCR tire is a load-bearing, pressurized torus reinforced with several thousand belt and body ply cords tailored to operate in tension; additionally, car tires undergo approximately 30 million fatigue cycles in 40,000 miles of service – which occasionally occur under non-optimal conditions of underinflation, overload and exceedingly high speed. Difficulties hindering precise predictive analyses of tread wear, fatigue limits and tire failure modes arise due to: finite rubber deformations; temperature- and frequency-dependent material properties; and spatially varying, multidimensional internal stresses.
The twofold purpose of the rubber matrix, from a structural engineering perspective, is to contain the air and transmit stress to the load-bearing tire cords. The tread, sidewall and other rubber components have unique and important functions, but load carrying is subordinate. Reinforcing carbon black and/or silica provide essential strength and stiffness to the rubbery matrix, but also cause hysteresis or internal friction – which is synonymous with energy loss and tire rolling resistance.
The circumferential and shear stiffness of the belt package, and not its ultimate strength, control the handling characteristics of the radial tire. Actually, belts tend to be over-designed for strength and rarely suffer, for example, burst failures. Belt stiffness is largely determined by the moduli and cross-sectional areas of the belt’s constituent cord-rubber components. Counterintuitively, cord angle variations in the range of commercial use are more important than cord modulus in contributing to belt properties. Also, the innocuous body ply material under the PCR belt forms an array of relatively rigid triangles that reinforces the tread region.
This process, known as triangulation, is well known to civil engineers and was recognized as such in the early radial tire patents of Michelin. These non-deforming triangles impart a many-fold stiffness increase to an otherwise compliant structure. If one removed the underlying body ply, the belt cords would pantograph as an assembly of non-rigid rhombuses, and such tires would behave as their bias ply counterparts. Because of more severe operational requirements for truck tires, triangulation is effected by means of three or more belt plies. Further triangulation is achieved in high-performance PCR tires via cap plies.
On the other hand, bead wire ultimate strength, and not stiffness, is the key design parameter for the wire bundle to bear inflation, centrifugal and other service loads – and especially so for resisting burst failures. The individual strands of small-diameter, high-tensile wire provide the bead with flexibility for mounting and the structural integrity to support body ply and turn-up ply cord tension. The adroit manipulation of bead filler height and hardness is used to promote either tire ride or handling, as needed. Overall body ply compliance is important for ride quality, and is largely controlled by cord twist, while ply cord strength controls sidewall impact and burst resistance.
Strength-to-weight and stiffness-to-weight ratios are commonly used aerospace design metrics that indicate the effectiveness of fiber reinforcements in structural applications where reduced weight, irrespective of cost, is important. These parameters are known as specific strength and specific modulus, respectively. Traditionally, aramids have the highest specific strength of any organic or inorganic fiber, while boron and graphite have the highest specific stiffness or modulus. In tire fabric terminology, the equivalent strength metric is known as tenacity – measured in grams per denier (gpd). Don’t be surprised that on this basis, cotton is just as strong as steel at 3.4gpd. Interestingly, the strongest fiber per unit weight known today (40% higher than aramid) is an ultra-high molecular weight polyethylene known commercially as Dyneema, but it is not suitable for use in tires due to its relatively low melting point (130°C). Just as power-to-weight ratios are important in future designs of jet engines and race cars, full exploitation of the specific strength and modulus potential of fibers currently available or yet to be developed could lead to meaningful reductions in tire weight – constrained, of course, by cost considerations.
