extrapolation is the process whereby we extend an established numerical relationship between two variables beyond the limits of our observed and recorded data. why extrapolation would not be useful and wise to use in force-elongation graph?
In force-elongation, as one extroplates outside the linear region, one enters the stress failure area, in which the curve vastly changes.
Extrapolation is not useful and wise to use in force-elongation graphs because it can lead to unreliable and inaccurate predictions. In a force-elongation graph, the linear region represents a consistent and predictable relationship between force and elongation. This linear region is typically the range in which the material behaves elastically, meaning it returns to its original shape after the applied force is removed.
However, once you move beyond the linear region, the behavior of the material can change significantly. This is often referred to as the stress failure area or the plastic region. In this area, the material starts to deform permanently and does not return to its original shape when the force is removed. The curve of the graph in this region can differ greatly from the linear portion.
When you extrapolate beyond the linear region, you are essentially assuming that the same relationship between force and elongation continues to hold, even though this assumption may not be valid. Extrapolation can lead to inaccurate predictions and may not represent the true behavior of the material. The curve can have sudden changes, unexpected behavior, or even failure of the material.
Therefore, it is not recommended to use extrapolation in force-elongation graphs because it can provide misleading information and unreliable predictions, especially when entering the stress failure area. Instead, it is better to rely on the data within the observed range and avoid making assumptions about the material's behavior beyond what is measured and recorded.