In the Master Curve brittle fracture model, it is assumed that the steel is macroscopically homoge­neous. In real wrought steels, the macro — and micro­structures are seldom fully homogeneous due to various effects occurring during production and cool­ing, such as segregation of elements and development ofinclusions. The resultant inhomogeneity may man­ifest itself as excessive data scatter. However, in welds or dissimilar metal joints, the material in the asso­ciated heat-affected zone (HAZ) may exhibit strongly distributed ‘inhomogeneity’ so that two or more sub­populations can be distinguished in the test data. Often in the final application of the fracture toughness data, it is only essential to determine a statistically sound conservative estimate for the lower bound frac­ture toughness, which can then be used to construct a conservative reference curve for the material.

In most cases, even those where materials show slight inhomogeneity, the standard Master Curve

estimation is sufficient, without further assessments. For testing the data population for possible inhomoge­neity, several approaches have been developed. A com­mon feature for all of these approaches is that they are based on the standard Master Curve, but are extended to properly take into account the inhomoge­neity. The following extended approaches have been proposed for analyzing inhomogeneous materials:

1. Simplified SINTAP procedure for determining a conservative lower bound estimate of fracture toughness when the inhomogeneity is of randomly distributed type.16,20

2. Bimodal or multimodal models for analyzing data­sets showing distributed inhomogeneity (typically welds and HAZ materials).17,20

3. Model for analyzing randomly inhomogeneous materials, including, for example, macroscopic

17,20

segregations.

Of the three methods, SINTAP is the simplest and the one recommended for initial assessment of the quality of data; it can generally be applied in conservative structural integrity analysis when material inhomoge­neity is suspected. An advantage of the SINTAP procedure is that it can be performed for a small dataset, unlike the bimodal or multimodal analyses, which require 15 or more data points for a valid assessment. It should be noted that the SINTAP analysis does not produce a statistically representa­tive description ofthe whole dataset, but its primary purpose is to determine whether the dataset is homogeneous and secondly, to develop a generally conservative lower bound when possible material inhomogeneity is present. The model for analyzing randomly distributed inhomogeneities gives a statis­tically correct description of the fracture toughness data, but requires a large dataset and is more com­plicated to perform than the SINTAP analysis. When there are a sufficient number of fracture toughness data points, the bimodal/multimodal and the randomly distributed inhomogeneous models should be used to better identify a more statistically correct description for a modified Master Curve.

The simplified SINTAP procedure is described next. The SINTAP analysis is based on the maximum likelihood method like the basic Master Curve pro­cedure and it consists of three steps as follows.

Step 1 is the standard estimation giving the first estimate of T0 and the median fracture toughness according to ASTM E 1921. The resulting T0 is used as an input value for Step 2.

Step 2 is a lower tail maximum likelihood estima­tion and is performed so that all data exceeding the median fracture toughness are censored by substituting d = 0 and by reducing the corresponding KJc values to the median curve. If the resulting new T0 (T0-2) is lower than the T0 from Step 1 (T0-1), then T)-sintap = T)_i; oth­erwise, Step 2 shall be repeated using the last T0 estimate (T0-2) as a new input value until a con­stant T0 (T0-2adj) is obtained. If the number of valid data is ten or more, T0-SINTAP = T0-2adj, otherwise Step 3 shall be performed.

Step 3 gives the minimum value estimate of T0 and is performed only if the number of valid test data is less than 10. In Step 3, an additional safety factor is incorporated for cases where the number of tests is small. Here, the value of T0 is estimated for each single data point to find the maximum value of T0 (T0 max). If the result­ing T0 max> T0-2 adj + 8 ° Q T0-SINTAP = T0 max, otherwise T0-SINTAP = T0—2 adj.

The steps and the data censoring in Steps 1 and 2 are described schematically in Figure 18. The flow chart of the iterative procedure is shown in Figure 19.