Rail residual stress distributions can be complex and variable in nature, as different manufacturing techniques produce varying stress magnitudes and distributions. To evaluate the effect of residual stresses on rail integrity, an analysis technique was sought that could quantify the effect of these stresses on web crack propagation.
To evaluate existing scientific knowledge of this problem, both an extensive literature review and discussions with industry personnel were conducted. These investigations revealed no generally accepted means for measuring residual stresses in rails that could readily be applied to evaluate the rail web-cracking problem. It should be noted, however, that a technique for evaluating tensile residual stresses based on cutting rails longitudinally down the web has been developed into a standard in Russia (the former USSR). The technique is based on the fact that, in the presence of tensile residual stresses, the rail head and base will bow away from each other. Measuring deflections of the rail ends, a rail rejection criteria was developed that required the end deflection between the head and base to be less than 3.7 mm for a specified saw cut length. While this approach qualitatively addresses residual stresses, it does not identify the magnitude of stresses necessary for a crack to progress unstably in the web.
A method for evaluating the potential for unstable growth of cracks in rail webs was developed using fracture mechanics principles. This methodology combines the effects of residual stress, crack length, and material fracture resistance to establish a failure criteria. The crack geometry and stresses in the rail web are characterized by the stress intensity factor, K. The resistance to fracture is described by the fracture toughness, KIC, a material property. The criterion for failure embodied in this approach is the stress intensity factor, K, equaling or exceeding the fracture toughness, KIC. That is, failure occurs if:
K > KIC ( K is greater than KIC )
Application of this approach required a means of determining an analytical expression for the stress intensity factor that could be applied to various rails. Standard test techniques were used to measure the fracture toughness, KIC.
The stress intensity factor for a cracked rail was determined using an approach developed by Wineman. This approach simulates rail web cracking with a longitudinal cut in the web. If tensile residual stresses are present, the head and base of the rail will bend away from one another. The degree of curvature of the head and base is related to the amount of bending, which in turn is related to the magnitude of the residual stresses.
The radius of curvature values before and after the saw cutting were determine by placing a beam on the rail with two points of contact, and then measuring the deflection normal to the rail head with a dial indicator at a location midway between the contact points. While this method accounts for the effect of residual stress on crack driving force, KI, the stresses do not have to be measured directly. Instead, K is determined by measuring simple geometric parameters.
This approach is valid for a rail in which both the base and head are free to deflect in an ?unconstrained? manner as the residual stresses are relieved during crack growth (or saw cutting). However, the bases of in-service rails are constrained by ties. The impact of the tie constraint was evaluated through finite element analysis, as described below. The analysis showed that the stress intensity factor for a constrained rail (i.e., in-service and attached to ties) is obtained by dividing the stress intensity factor for the unconstrained rail by the square root of 2 ( sqrt(2) = 1.414).
To evaluate this approach, stress intensity factors and fracture toughness values were determined for rails from two different manufacturers. Rails with various dates of manufacture and heat treatments were considered. Additionally, because end deflections are easier to measure in the field than curvatures, end deflections were measured to determine whether a correlation could be made with the fracture mechanics approach.
The stress intensity factor for a rail with suitable crack size is dependent on the residual stress state. The effect of this stress state on the stress intensity factor can be determined solely by measuring the difference in curvature of the rails in the cracked and uncracked conditions.
In this investigation, a 42 inch section was removed from each rail and a crack was simulated by a 36-inch-long saw cut made along the neutral axis of the web. Deflection measurements were made on the head and base of the rail using a deflection gage consisting of a 10-inch-long straight beam with a dial indicator mounted at the center. Feet at each end of the beam provided a simple support condition and a small standoff from the rail.
Curvature measurements were taken at eleven locations on the base and head of each rail specimen in both the uncracked and cracked (saw cut) conditions. Three readings were made at each location, and the average of the three was used in the stress intensity factor calculations. Measurements were made at a minimum of 13.75 inches from the free end of the rail and a minimum of 12.25 inches from the end of the saw cut. This was done to help minimize any end effects on the stress intensity factor evaluations.
While the stress intensity factor/fracture toughness approach is useful from an analytical perspective, it has limited use for railroad personnel whose job it is to determine whether a particular heat of rails should be accepted. Consequently, an approach was developed to make this determination using a combination of simple dimensional measurements (which can be made in a maintenance shop) combined with material property (fracture toughness) data.
When rails were cut longitudinally through the web, the ends will deflect away from each other when tensile residual stresses are present. Because end deflections are easier to measure in the field than curvature calculations, a relationship between end deflections and stress intensity factors would be useful in developing a practical screening procedure. To this end, a series of plots of end deflection at various saw cut lengths vs. stress intensity factor were constructed. A linear relationship between end displacement and the long-crack (plateau) stress intensity factor is evident from this data. Combining this data with the measured fracture toughness for the rail, the previously mentioned failure criterion can be applied.
Tensile residual stresses in railroad rail are frequently a byproduct of rail manufacturing and heat treating processes. If these stresses are tensile in the rail web, they can cause cracks that may be present to grow unstably, causing the separation of the rail head from the base. To evaluate this possibility, a technique has been presented which quantifies the effect of web stresses on crack stability. Using fracture mechanics principles, this method characterizes a failure criterion in terms of the stress intensity factor due to the residual stresses and the fracture toughness of the specific rail material as processed. Rail failure will occur if: K > KIC. This criterion was then used to develop a methodology that can be used by plant personnel for screening rails.
After analyzing over 50 rails from different manufacturers, heats, and dates of manufacture, the following observations were made:
It was recognized that fracture mechanics provided a means of characterizing the problem using measurements of curvature from the rail with a saw-cut web. However, this technique was impractical for use in the field by railroad personnel. Consequently, an equivalent approach was devised involving end deflections of the cut rail (which are more easily measured) and the rail-steel fracture toughness.
The purpose of the procedure presented in this paper is to assess the severity of tensile residual stresses in the rails. It is possible to reduce or eliminate tensile residual stresses by changes in processes used for the manufacture and heat treatment of the rails. Process steps, such as quenching, directly affect the cooling rate of the rail. The differential cooling associated with quenching is one of the factors that controls the final residual stress state. Manufacturing processes should be refined such that the residual stresses in the web are compressive or at least reduced if they are tensile. It is possible to fully eliminate the web-cracking problem through manufacturing process improvements.
T. Kim Parnell, PhD, PE is a Mechanical Engineering consultant with strong experience in a number of technology areas. He holds PhD and MSME degrees from Stanford University in Mechanical Engineering. Dr. Parnell specializes in the mechanical engineering design and behavior of Biomedical Devices, Shape Memory Metals, Bioabsorbable Polymers, MEMs, Electronic, and Miniature Components. He consults actively in these areas, as well as in failure analysis and reliability.
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