| Summary: | Temperature has a great influence on the mechanical properties of ductile cast iron or nodular cast iron. A thermomechanical treatment was carried out at various elevated temperatures of 450 °C, 750 °C and 850 °C using a universal testing machine with a tub furnace. Specimens were held at these temperatures for 20 min to ensure a homogeneous temperature distribution along the entire length of the specimen, before a tensile load was applied. Specimens were deformed to various levels of uniform strain (0%, 25%, 50%, 75%, and 100%). These degrees of deformation were measured with a dial gauge attached to a movable cross plate. Three strain rates were used for each specimen and temperature: <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1.8</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>4</mn></mrow></msup><mo> </mo><msup><mrow><mi mathvariant="normal">s</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>9</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>4</mn></mrow></msup><mo> </mo><msup><mrow><mi mathvariant="normal">s</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>4.5</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>3</mn></mrow></msup><mo> </mo><msup><mrow><mi mathvariant="normal">s</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></semantics></math></inline-formula>. A simple analytical model was extracted based on the CT tensile test geometry and yield stress and a 0.2% offset strain to measure the fracture toughness (J<sub>IC</sub>). To validate the analytical model, an extended finite element method (XFEM) was implemented for specimens tested at different temperatures, with a strain rate of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1.8</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>4</mn></mrow></msup><mo> </mo><msup><mrow><mi mathvariant="normal">s</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></semantics></math></inline-formula>. The model was then extended to include the tested specimens at other strain rates. The results show that increasing strain rates and temperature, especially at 850 °C, increased the ductility of the cast iron and thus its formability. The largest percentage strains were 1 and 1.5 at a temperature of 750 °C and a strain rate of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1.8</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>4</mn></mrow></msup><mo> </mo><msup><mrow><mi mathvariant="normal">s</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>9</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>4</mn></mrow></msup><mo> </mo><msup><mrow><mi mathvariant="normal">s</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>,</mo></mrow></semantics></math></inline-formula> respectively, and reached their maximum value of 1.7 and 2.2% at 850 °C and a strain rate of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>9</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>4</mn></mrow></msup><mo> </mo><msup><mrow><mi mathvariant="normal">s</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>4.5</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>3</mn></mrow></msup><mo> </mo><msup><mrow><mi mathvariant="normal">s</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>,</mo></mrow></semantics></math></inline-formula> respectively. In addition, the simple and fast analytical model is useful in selecting materials for determining the fracture toughness (J<sub>IC</sub>) at various elevated temperatures and different strain rates.
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