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where they drop first and then increase very sharply in the
transition zone. This behavior is attributed to the tube
deformation elbow in this area (Fig. 4).
Due to tubesheet spring back after releasing the load, the
hoop stress (rh) on both inner and outer surfaces is found to
be compressive in most of the rolled tube length, but
becomes tensile in the transition zone where it reaches a
value of about half the yield strength of the material on the
inner surface of the tube. The axial stress which remains
very small in magnitude on both surfaces becomes tensile
on the inner surface in the transition zone as well after roller retraction, reaching a value of 100 MPa. It should be
noted that the tensile hoop and axial stress maxima happen
at the same axial position around 8 mm from the end of the
rolled area (Fig. 5b). This is somehow different from what
was reported by Williams (1997). The existence of high
tensile hoop and axial stresses in this region when coupled
with expected tensile hoop stress from inner fluid pressure
make it a critical design zone that needs proper attention
especially when using aggressive fluids.
Analysis of the tube’s outer surface stress distribution
after roller retraction showed that rz reaches an average
tensile stress value of 9 MPa which drops to 5 MPa upon
the release of load which are very small compared to rr and
rh and emphasizes the assumption of this case as a plane
stress model. The contact stress which reached an average
compressive value of 160 MPa after the last loading step
drops to 61 MPa upon unloading (Fig. 5a). Because this
stress is a measure of the joint strength its variation with
initial clearance and material strain hardening is studied in
detail in the following section.
Effect of clearance and tube material strain hardening
on residual contact stress
The combined effects of clearance and tube material strain
hardening on the average value of radial stress for 5% wall
reduction obtained from the 3-D finite element model are
illustrated in Fig. 6. As can be seen, the clearance range
considered in this study is well above the TEMA overtol-
erance limit. Similar to what was observed in axisymmetric
model results by Al-Aboodi et al. (2008) for strain hard-
ening tube materials (Ett[0 GPa), the residual contact
stress gradually increases with the increase in radial
clearance before dropping at lower cut-off clearances. The
increase in residual contact stress with increase in Ett is due
to higher tube material strength resisting tubesheet material
spring back.
As illustrated in Fig. 7, the 3-D model resulted in lower
critical (cut-off) clearances for both types of tube materials
(Ett = 0 GPa and Ett = 1.2 GPa) and higher contact
stresses for strain hardening material than the axisymmetric
model. This discrepancy comes from the difference
between the calculated wall reduction and the actual one.
The same value of input displacement will result in lower
value of actual percent wall reduction for the 3-D model
because of the extra tangential displacement in the 3-D
model. Subsequently, the critical clearance will be higher
for axisymmetric model.
Experimental validation of contact stress
In the experimental work the joint strength is measured in 摘要：在石化工厂，重复去管和加管的热交换器在它有用的寿命期间可能导致过大的管板孔与最大容忍度超过管式换热器制造协会（特马）标准（1988）的规定。在这些过大的管子里，由于减少管与管板之间的界面压力，滚轴的扩张可能导致管子变薄和削弱的联合。在目前的工作中，一个管和管板联合的三文有限元（FE）模型被用来确定沿滚轴的轴向方向扩大的管和管板联合的位移和应力分布和评估在界面压力和管变形下管材料的初始最大间隙和应变硬化的联合效果。从目前的模型获得的结果，把轴对称有限元分析和实验结果进行比较。轴对称和三文模型屈服可比趋势表明弹性完全塑性管材料的残余接触压力保持不变并远高于规定的特马最大容忍值。此外，这两个模型表明了应变硬化管材料的界面压力随间隙的增加而增加。由观察得出一个明显的区别是在高容忍度时3d模型预测截止许可（间隙的界面压力开始大幅下降）低于30%的轴对称模型。从3d结果与实验测试进行比较，预测到管内表面变形和去掉力。23311