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A diagram illustrates a circular cross-section with an inner elastic zone and an outer plastic zone, accompanied by a graph showing torque increasing linearly with radius up to a critical value.

Alt text: A diagram showing a circular cross-section divided into elastic and plastic zones, alongside a graph representing the relationship between applied torque and radial distance.

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  • The diagram depicts a circular cross-section that is conceptually divided into two regions: an inner, dashed circle labeled "elastic zone" and an outer ring labeled "plastic zone".
  • Radial lines extending from the center indicate the radii \(r_e\) and \(R\). The radius \(r_e\) marks the boundary between the elastic and plastic zones, while \(R\) represents the outer radius of the object.
  • Below the circular diagram is a graph plotting torque, denoted by the symbol \(\tau\), on the vertical axis, against radial distance on the horizontal axis.
  • The graph shows that the torque \(\tau\) is zero at a radial distance of zero. As the distance increases, the torque increases linearly, reaching a constant value, \(\tau_y\), at the radius \(r_e\). This value \(\tau_y\) corresponds to the transition between the two zones.
  • The graph maintains the constant torque value \(\tau_y\) across the entire range from \(r_e\) to \(R\).

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