Issue 50

A. Kakaliagos et alii, Frattura ed Integrità Strutturale, 50 (2019) 481-496; DOI: 10.3221/IGF-ESIS.50.40 493 towards chamber exterior surface. Additionally, the mechanical properties and associated material strength of bronze are not influenced by temperature up to approximately 200 o C. Exceeding this temperature, a gradual drop of material strength and properties is expected. (a) (b) Figure 8: (a) Cannonball velocity inside Bombard bore; (b) Temperature inside powder chamber. For subsequent evaluation of temperature effects combined with powder chamber stresses due to internal pressure the powder chamber was set conservatively in a condition of steady heat flow. Herein, the temperature T o is the temperature of the inner surface of the chamber cylinder, whereby, the temperature on the outer surface is set at zero. T o is set at 200 o C as evaluated previously and reflects the temperature difference between the temperature at the end of the event and the ambient temperature at 20 o C. In this situation the temperature T at any point inside the powder chamber solid, with distance r from the center of the cylinder is expressed with Eq.(19), whereby the resulting tangential stress σ 1 , radial stress σ 2 and axial stress σ 3 are evaluated with Eqs.(20-22), with Poisson’s ratio ν=0.3 and coefficient of linear expansion for bronze α t =20×10 -6 o C -1 (Timoshenko and Goodier [13]). The corresponding radial displacement δ T at any point located at a certain radial distance r can be evaluated with Eq.(23) (Vullo [ 14]): ൌ ் ೚ ௟௡ሺ௔ ௕⁄ ሻ ቀ ௔ ௥ ቁ where: ൑ ൑ (19) ଵ ൌ ఈ ೟ ா் ೚ ଶሺଵି௩ሻ௟௡ሺ௔ ௕⁄ ሻ ൈ ቂ1 െ ቀ ௔ ௥ ቁ െ ௕ మ ௔ మ ି௕ మ ቀ1 െ ௔ మ ௥ మ ቁ ቀ ௔ ௕ ቁቃ (20) ଶ ൌ ఈ ೟ ா் ೚ ଶሺଵି௩ሻ௟௡ሺ௔ ௕⁄ ሻ ൈ ቂെ ቀ ௔ ௥ ቁ െ ௕ మ ௔ మ ି௕ మ ቀ1 െ ௔ మ ௥ మ ቁ ቀ ௔ ௕ ቁቃ (21) ଷ ൌ ఈ ೟ ா் ೚ ଶሺଵି௩ሻ௟௡ሺ௔ ௕⁄ ሻ ൈ ቂ1 െ 2 ቀ ௔ ௥ ቁ െ ଶ௕ మ ௔ మ ି௕ మ ቀ ௔ ௕ ቁቃ (22) ் ൌ ఈ ೟ ሺଵାఔሻ௥் ೚ ଶሺଵିఔሻ୪୬ ሺఈ ௕ሻ⁄ ൈ ቂሺ1 െ ሻ ൅ ቀ ఈ ௥ ቁ െ ௕ మ ఈ మ ି௕ మ ቀ ఈ ௕ ቁ ቀ ఈ మ ௥ మ ൅ 1 െ 2 ቁቃ (23) The von Mises combined stress resulting from the individual chamber temperature stresses from Eqs.(20-21) was evaluated in Fig.9. Herein, the situation at 200 o C yields a significant plastic zone extending from 286 mm till chamber exterior surface. This effect is marginally pronounced at temperature 400 o C, a value close to the average temperature at 389 o C evaluated previously. With the cooling effort by the bombard crew, the von Mises combined stress would gradually drop from 200 o C, the temperature after the shot at 2.5 sec, thus, effectively bringing the developed combined stress below yield at 100 o C (Fig.9).