Zhuojin Pipe Fitting Co., LtdResidual Stress Effects of Cold-Rolled Seamless Steel Pipes on Hydraulic Cylinder Load-Bearing Capacity
Overview of the Study
This research by Bao Yan, Ye Jindu, Ma Xu, and Zhang Chunqiu from Tianjin University of Technology investigates the impact of residual stresses introduced during the cold-rolling forming process on the load-bearing capacity of hydraulic cylinder tubes. Funded by the National Natural Science Foundation of China (Grant No. 50975205) and the Tianjin Science and Technology Development Plan (Grant No. 12ZCZDGX00600), the study employed nonlinear finite element analysis to quantitatively evaluate how residual stresses interact with working stresses under internal hydraulic pressure. The central finding is striking: the presence of initial residual stresses changes the magnitude and distribution of equivalent stress in the cylinder tube, with the maximum equivalent stress reaching three times that of a stress-free tube, thereby significantly reducing load-bearing capacity. The authors recommend that cold-rolled steel pipes used for hydraulic cylinders must undergo heat treatment to eliminate residual stresses before service.
Technical Background and Methodology
Cold rolling is a widely used forming process for seamless steel pipes, particularly for producing tubes with tight dimensional tolerances and high surface finish required for hydraulic cylinder applications. During cold rolling, the pipe is plastically deformed by a rotating roll to reduce its diameter and/or wall thickness. This plastic deformation inevitably introduces residual stresses into the material due to the non-uniform strain distribution across the wall thickness and around the circumference. Upon unloading (demolding), the elastic recovery of the differently strained regions creates a self-equilibrating residual stress field.
The study methodology involved three key steps:
- Cold-rolling process simulation: The forming process was simulated to obtain the residual stress distribution in the pipe after demolding. This involved modeling the contact between the roll and the pipe, the plastic deformation of the pipe material, and the subsequent elastic unloading.
- Working stress analysis: After obtaining the residual stress field, internal hydraulic pressure was applied to the inner surface of the pipe to simulate working conditions. The combined stress field (residual + working) was computed.
- Comparison with stress-free case: A reference analysis was performed on an identical pipe without residual stresses under the same internal pressure, allowing direct comparison of stress distributions and load-bearing capacity.
Key Results and Stress Distribution
| Condition | Maximum Equivalent Stress (MPa) | Stress Distribution Pattern | Load-Bearing Capacity Relative Value |
|---|---|---|---|
| Stress-free pipe under internal pressure | Baseline | Hoop stress dominant, uniform across wall | Reference (1.0) |
| Cold-rolled pipe with residual stress under internal pressure | ~3× baseline | Complex redistribution, peak at inner surface | Significantly reduced |
| Cold-rolled pipe without heat treatment | High tensile residual at inner surface | Compressive outer surface, tensile inner surface | Degraded |
The residual stress pattern in cold-rolled pipes typically features tensile stresses at the inner surface and compressive stresses at the outer surface. This is because the inner surface undergoes greater plastic compression during rolling (as the roll compresses the material from the outside), and upon elastic unloading, the inner surface rebounds more than the outer surface, creating a net tensile residual stress at the bore. When internal hydraulic pressure is subsequently applied, the hoop stress (which is tensile and maximum at the inner surface) superimposes on the existing tensile residual stress, leading to a dramatically higher combined stress state.
Engineering Significance and Practical Countermeasures
Impact on Hydraulic Cylinder Performance
Hydraulic cylinders operate under cyclic internal pressure loads, and the load-bearing capacity of the cylinder tube is directly related to the onset of yielding. When residual tensile stresses are present at the inner surface, the effective stress level under a given hydraulic pressure is higher than predicted by classical thick-walled cylinder theory (Lame's equations). This means:
- The cylinder reaches its yield limit at a lower operating pressure than expected.
- Fatigue crack initiation is accelerated at the inner surface where tensile residual stresses concentrate.
- The safety factor calculated using standard formulas without residual stress correction is non-conservative and potentially dangerous.
Recommended Countermeasures
- Post-rolling heat treatment: The primary recommendation from the study is to apply stress-relief heat treatment after cold rolling. Typical parameters include:
- Temperature: 550–650°C (below the lower critical temperature A1)
- Soak time: 1–2 hours per 25 mm of wall thickness
- Cooling rate: Furnace cool or controlled air cool
- Controlled cold rolling parameters: Reducing the reduction ratio per pass, increasing the number of passes, and using optimized roll geometry can minimize the magnitude of residual stresses introduced during forming.
- Shot peening or laser peening: If heat treatment is not feasible due to dimensional tolerance requirements, surface treatment methods can introduce beneficial compressive residual stresses that counteract the tensile residual stresses from rolling.
- Residual stress measurement: Engineers should incorporate residual stress measurement (e.g., X-ray diffraction, hole drilling method) into the quality control process for critical hydraulic cylinder tubes.
FMEA Analysis of Residual Stress-Related Failures
| Failure Mode | Cause | Effect | Detection Method | Countermeasure |
|---|---|---|---|---|
| Premature yielding | High tensile residual stress at bore | Cylinder tube deformation under normal pressure | Pressure test, strain measurement | Heat treatment |
| Fatigue crack initiation | Stress concentration at bore | Cyclic failure under pressure cycling | Dye penetrant, ultrasonic testing | Stress relief + surface treatment |
| Dimensional distortion | Uneven residual stress release during machining | Out-of-round bore, out-of-spec diameter | CMM inspection, bore gauge | Controlled cooling, stress relief before machining |
Study Insights and Recommendations
This study provides a compelling quantitative demonstration of the detrimental effects of residual stresses in cold-rolled hydraulic cylinder tubes. The finding that maximum equivalent stress can reach three times the stress-free value is particularly alarming from a safety perspective. For steel pipe manufacturers, this underscores the necessity of integrating residual stress management into the production process as a standard practice rather than an optional quality enhancement. The nonlinear FEM approach used in this study offers a powerful tool for predicting the combined stress state, but it requires accurate material properties and boundary conditions. In practice, engineers should combine FEM predictions with experimental validation (such as ring expansion tests or split-ring tests) to verify residual stress levels. The recommendation for mandatory heat treatment of cold-rolled hydraulic cylinder tubes should be adopted in industry standards and quality specifications. Furthermore, the study highlights the importance of process simulation in predicting residual stress patterns during forming, which can guide process optimization to minimize residual stresses at the source. This research is a valuable contribution to the field of pressure vessel and hydraulic cylinder engineering, bridging the gap between forming process technology and structural performance assessment.