Cast steel joints are increasingly adopted in large-span and high-rise steel structures, as well as in bridge engineering, due to their excellent geometric flexibility, smooth force transition, and favorable overall performance. However, during the casting process, internal discontinuities such as shrinkage pores, gas holes, inclusions, and micro-cracks are almost unavoidable. These imperfections, collectively referred to as casting defects, may influence the mechanical response of the component under both static and cyclic loads. In many practical engineering applications, cast steel joints are allowed to work with certain levels of defects, which makes the assessment of the effect of casting defects on the structural integrity a critical issue. I therefore conducted a comprehensive numerical investigation to evaluate how the grade size, the position, and the distribution of casting defects affect the static and fatigue performance of a steel truss structure connected by cast steel nodes. The results are important for improving current casting quality evaluation procedures.
Modern foundries employ advanced automatic pouring and solidification control techniques to reduce the formation of casting defects. A typical automatic pouring line is shown in the following figure.
Nevertheless, even with strict process control, some defects remain. The present study models spherical gas pores as representative casting defects. The size and location of these defects on the cast steel joint were determined according to the classification rules in the Chinese national standard GB/T 7233—2009 for ultrasonic testing and quality grading of steel castings. In this standard, the evaluation area is set to 317 mm × 317 mm (approximately 100,000 mm²) placed at the region with the most severe defects. Based on the projected area and through-thickness dimension of the largest defect inside the evaluation frame, the casting quality is categorized into five grades, with Grade 1 being the best and Grade 5 the worst. Because gas porosity is one of the most common casting defects and has a well-defined spherical shape, it was chosen as the defect type in all models.
To investigate the influence of casting defects on the structural behavior, I built a four-bay steel truss model. The upper chord was a hot-rolled I-section (Chinese profile 50a), the lower chord was a steel tube with a wall thickness of 20 mm, and the diagonal braces were steel tubes with a wall thickness of 16 mm. The cast steel joint, made of GS-20Mn5V cast steel, connected the lower chord and the braces. A concentrated load was applied at the midspan of the upper chord. The relevant geometric parameters are summarized in the following table.
| Parameter | Value |
|---|---|
| Number of bays | 4 |
| Bay length | 2200 mm |
| Total length | 8800 mm |
| Upper chord section | I-section 50a |
| Lower chord wall thickness | 20 mm |
| Diagonal brace wall thickness | 16 mm |
| Applied static load F | 1000 kN |
Because the cast steel joint has a complex geometry and the casting defects are small and randomly positioned, it was difficult to build the model directly using a commercial finite element package such as ANSYS. I therefore used SolidWorks to create the full three-dimensional solid model of the steel truss containing the cast steel joint and the defects, and then imported the geometry into ANSYS for meshing and analysis. The finite element mesh was generated using 10-node tetrahedral elements (Solid187). Different regions were assigned different mesh sizes for accuracy and efficiency. The regions of the upper chord, tubes, cast steel joint, and the vicinity of the casting defects were discretized with gradually finer mesh sizes.
Mesh Sensitivity Analysis
Before performing systematic studies, I carried out a mesh sensitivity analysis to determine an appropriate mesh density. A single Grade 2 casting defect was introduced at a representative location (position ②) on the cast steel joint. Four sets of mesh sizes were considered, as listed below. The same loading condition was applied, and the maximum Mises stress and the displacement field were compared.
| Model region | Set 1 (mm) | Set 2 (mm) | Set 3 (mm) | Set 4 (mm) |
|---|---|---|---|---|
| Upper chord (I-section) | 50 | 79 | 79 | 100 |
| Steel tubes | 15 | 20 | 30 | 40 |
| Cast steel joint | 10 | 15 | 20 | 30 |
| Near the casting defect | 1 | 2 | 4 | 5 |
The computed results for Sets 1, 2, and 3 were nearly identical, while Set 4 gave visibly different stress and displacement values. Thus, Set 3 was deemed sufficiently accurate and was adopted for all subsequent calculations because it provides a good balance between computational effort and accuracy.
Static Behavior of the Structure with Casting Defects
In the static analysis, a concentrated force \(F = 1000\,\text{kN}\) was applied vertically downward at the middle of the upper chord. The maximum Mises stress was used to characterize the static strength, and the maximum displacement was used to characterize the static stiffness. The reference model without any casting defect had a maximum stress of 180 MPa and a maximum displacement of 8.11 mm.
Effect of the Position of a Single Casting Defect
Nine models were created, each containing a single Grade 2 casting defect at one of the nine defect-prone positions (①–⑨) on the cast steel joint. The overall stress distributions of all nine models were very similar. The maximum stress in the cast steel joint ranged from 180 to 201 MPa, which is only a small variation compared with the defect-free value of 180 MPa. However, in the local region immediately around the defect, strong stress concentration occurred, and the local stress pattern varied significantly with the defect position. In terms of stiffness, the displacement clouds of the models with defects were virtually the same as those of the defect-free model. The deflection was largest at the midspan and decreased towards the supports. Therefore, the position of a single casting defect has a negligible influence on the overall static strength and stiffness of the truss, although it affects the local stress distribution.
Effect of the Size of a Single Casting Defect
To investigate the influence of defect size, I introduced a single Grade 3 defect at positions ①, ②, ③, ④, and ⑨. The computed maximum Mises stresses are compared with those for a Grade 2 defect at the same positions in the following table.
| Model | Defect position | Defect grade | Maximum Mises stress (MPa) |
|---|---|---|---|
| 1 | ① | Grade 2 | 200 |
| 2 | ① | Grade 3 | 202 |
| 3 | ② | Grade 2 | 182 |
| 4 | ② | Grade 3 | 182 |
| 5 | ③ | Grade 2 | 182 |
| 6 | ③ | Grade 3 | 182 |
| 7 | ④ | Grade 2 | 180 |
| 8 | ④ | Grade 3 | 183 |
| 9 | ⑨ | Grade 2 | 200 |
| 10 | ⑨ | Grade 3 | 200 |
As shown in the table, changing the defect from Grade 2 to Grade 3 alters the maximum stress by only about 1.7% at most. Similarly, the displacement fields are almost unchanged. Consequently, the defect size has a very limited effect on the static strength and stiffness of the structure.
Effect of Multiple Casting Defects
Real castings often contain several defects at different locations. To study the combined effect, I generated five models with multiple Grade 2 defects. The defect position combinations and the resulting maximum Mises stresses are listed below.
| Model | Defect positions | Defect grade | Maximum Mises stress (MPa) |
|---|---|---|---|
| 11 | ①, ②, ③ | Grade 2 | 182 |
| 12 | ①, ③, ④ | Grade 2 | 198 |
| 13 | ②, ⑦, ⑨ | Grade 2 | 182 |
| 14 | ④, ⑤, ⑥ | Grade 2 | 183 |
| 15 | ①, ②, ③, ⑧, ⑨ | Grade 2 | 186 |
All models remained elastic, since the maximum stress was well below the yield strength of GS-20Mn5V (280 MPa). The presence of multiple casting defects did not cause any noticeable change in the overall stress distribution. However, the maximum stress was somewhat dependent on which positions contained defects. For instance, Models 11, 12, and 15 all contained a defect at position ①, yet their maximum stresses were 182, 198, and 186 MPa, respectively, whereas a single defect at position ① gave 200 MPa. This indicates that the interaction between multiple casting defects can slightly modify the peak stress, but the effect is still small for static loading.
According to the GB/T 7233—2009 quality grading standard, Models 11 through 15 would all be classified as Grade 2 because the largest individual defect in each model satisfies the Grade 2 limit. Models 2, 4, 6, 8, and 10, each containing a single Grade 3 defect, would be Grade 3. Thus, the Standard grading implies that Models 11–15 are of better quality than Models 2, 4, 6, 8, and 10. However, if one ranks these models by their static strength (i.e., by the maximum stress), the order becomes: Model 4 = Model 6 = Model 11 = Model 13 > Model 8 = Model 14 > Model 15 > Model 12 > Model 10 > Model 2. This discrepancy reveals a major limitation of the current casting quality evaluation method: it focuses only on the most severe defect size and ignores the defect position and distribution. A more rational evaluation should consider the actual stress state in the neighborhood of the defect.
Fatigue Behavior of the Structure with Casting Defects
Static loads are not the only concern for real structures; most civil engineering structures experience repeated or cyclic loading over their service life. Fatigue damage is governed by local stress concentrations, and casting defects act as stress raisers that can dramatically reduce the fatigue life. Therefore, I performed constant-amplitude fatigue analyses on the same truss models. The fatigue load was applied at the same location as the static load, with a maximum load \(f_{\max} = 1000\,\text{kN}\) and a minimum load \(f_{\min} = -1000\,\text{kN}\), resulting in a fully reversed load cycle.
Modified S-N Curve for the Cast Steel Joint
The material under consideration is GS-20Mn5V cast steel. Fatigue tests on smooth specimens of this material, as reported in the literature, provided the S-N curve with a 95% confidence level. The lower-bound curve is used here to be conservative. The original material S-N curves are expressed as:
$$
\lg N =
\begin{cases}
36.7591 – 13.0055\,\lg S, & \text{upper},\\[4pt]
34.5727 – 12.1917\,\lg S, & \text{mean},\\[4pt]
28.9028 – 9.9581\,\lg S, & \text{lower},
\end{cases}
$$
where \(S\) is the nominal stress amplitude in MPa. Since the cast steel joint contains a casting defect, the local stress at the defect tip is higher than the nominal stress. I therefore modified the lower-bound S-N curve by introducing a correction factor \(K_{\sigma D}\) that accounts for the size effect and the surface finish of the joint. The corrected fatigue life curve is
$$
\lg N = 28.9028 – 9.9581\,\lg (S\,K_{\sigma D}).
$$
The associated fatigue limit becomes
$$
\sigma_{-1D} = \frac{\sigma_{-1}}{K_{\sigma D}},
$$
where \(\sigma_{-1}\) is the fatigue limit of the smooth specimen. The correction factor is defined as
$$
K_{\sigma D} = \frac{K_{\sigma s}}{\varepsilon \beta_1},
$$
where \(K_{\sigma s}\) is the fatigue notch factor for the surface roughness. Because the stress extracted from the finite element model is already the local stress at the defect, \(K_{\sigma s}\) is taken as 1. The term \(\varepsilon\) is the size factor, which depends on the thickness of the joint at the defect location. The coefficient \(\beta_1\) is the surface finish factor, taken as 0.65 based on the machining quality of cast steel surfaces. The size factor at each defect position is given in the following table.
| Defect position | Size factor \(\varepsilon\) |
|---|---|
| ①, ⑨ | 0.95 |
| ②, ④, ⑧ | 0.90 |
| ③, ⑤ | 0.83 |
| ⑥ | 0.82 |
| ⑦ | 0.80 |
Using these size factors, I obtained the modified S-N curves corresponding to each defect position. The curves are displayed in the following table conceptually, but the fatigue life values were computed directly from the equations. The modified curves show that for a given stress amplitude, a defect at position ③ or ⑤ leads to a lower fatigue life than a defect at position ① or ⑨, because the larger size factor reduces the correction factor and increases the fatigue strength? Actually the correction factor is inversely proportional to \(\varepsilon\) and \(\beta_1\), so smaller \(\varepsilon\) gives larger \(K_{\sigma D}\), which decreases the fatigue life. Thus, a defect at position ⑦, where \(\varepsilon=0.80\), has the most detrimental effect.
Effect of the Position of a Single Casting Defect on Fatigue Life
Nine models with a single Grade 2 casting defect at positions ①–⑨ were analyzed under the constant-amplitude fatigue load. The maximum stress amplitude at each defect location was extracted from the finite element solution and used with the corresponding modified S-N curve to estimate the local fatigue life. The results are summarized below.
| Model | Defect position | Defect grade | Fatigue life (×10⁵ cycles) |
|---|---|---|---|
| A | ① | Grade 2 | 2.43 |
| B | ② | Grade 2 | 3.49 |
| C | ③ | Grade 2 | 1.91 |
| D | ④ | Grade 2 | — |
| E | ⑤ | Grade 2 | — |
| F | ⑥ | Grade 2 | — |
| G | ⑦ | Grade 2 | — |
| H | ⑧ | Grade 2 | 49.4 |
| I | ⑨ | Grade 2 | 23.65 |
In the table, “—” means that the stress amplitude at the defect is below the modified fatigue limit, so the joint has an infinite fatigue life under the given load. The results show a remarkably strong dependence of fatigue life on the defect position. Even though all nine models have the same defect grade (Grade 2), the fatigue lives differ by several orders of magnitude. For example, the life for a defect at position ③ is \(1.91 \times 10^5\) cycles, while positions ④, ⑤, ⑥, and ⑦ give infinite life. The fatigue life for a defect at position ① is \(2.43 \times 10^5\) cycles, whereas a defect at position ⑧ yields \(4.94 \times 10^6\) cycles, almost two orders of magnitude higher. Therefore, the position of a casting defect is a primary factor that must be included in any fatigue-oriented quality evaluation.
Effect of the Size of a Single Casting Defect on Fatigue Life
To examine the influence of defect grade, I replaced the Grade 2 defect by a Grade 3 defect at positions ①, ③, ④, and ⑨, and reran the fatigue analyses. The resulting fatigue lives are listed below, together with the corresponding Grade 2 results from the previous table for direct comparison.
| Model | Defect position | Defect grade | Fatigue life (×10⁵ cycles) |
|---|---|---|---|
| J | ① | Grade 3 | 0.55 |
| K | ③ | Grade 3 | 0.68 |
| L | ④ | Grade 3 | — |
| M | ⑨ | Grade 3 | 2.90 |
For a fixed position, the higher defect grade (larger defect size) significantly reduces the fatigue life. For instance, at position ①, changing from Grade 2 to Grade 3 reduces the life from \(2.43 \times 10^5\) to \(5.5 \times 10^4\) cycles, i.e., a reduction of about 77%. At position ③, the life drops from \(1.91 \times 10^5\) to \(6.8 \times 10^4\) cycles. At position ⑨, the life drops from \(2.365 \times 10^6\) to \(2.9 \times 10^5\) cycles, which is nearly one order of magnitude. Thus, the defect size has a strong impact on the fatigue performance, although its effect on static strength is minor.
Effect of the Distribution of Multiple Casting Defects on Fatigue Life
Since real castings usually contain multiple defects, I investigated four models with several Grade 2 defects at different combinations of positions. The fatigue lives at the primary defect locations are summarized in the following table.
| Model | Defect positions | Defect grade | Fatigue life (×10⁵ cycles) |
|---|---|---|---|
| N | ①, ②, ③ | Grade 2 | ①: 0.34, ②: 1.64, ③: 1.64 |
| O | ①, ③, ④ | Grade 2 | ①: 0.32, ③: 1.64, ④: — |
| P | ②, ⑧, ⑨ | Grade 2 | ②: 1.52, ⑧: —, ⑨: 8.67 |
| Q | ①, ②, ③, ⑧, ⑨ | Grade 2 | ①: 0.36, ②: 1.64, ③: 1.64, ⑧: —, ⑨: 8.67 |
Comparing the life of each defect location in the multi-defect models with the single-defect models reveals a clear detrimental interaction effect. For example, a single Grade 2 defect at position ① gave a fatigue life of \(2.43 \times 10^5\) cycles, but when other defects coexist at positions ② and ③, the life at position ① drops to about \(0.34 \times 10^5\) cycles. Similarly, a single defect at position ② provided \(3.49 \times 10^5\) cycles, whereas in Model N the life at position ② is only \(1.64 \times 10^5\) cycles, and in Model P it is \(1.52 \times 10^5\) cycles. These results indicate that the presence of additional casting defects at neighboring positions intensifies the local strain field and accelerates fatigue crack initiation at the primary defect. Consequently, the fatigue performance of a cast steel joint with multiple casting defects is always worse than that of a joint containing only one isolated defect, even if the defect grade and position of that isolated defect are identical.
The table above also demonstrates that the fatigue life at a given defect position can vary by as much as a factor of about 7 depending on the distribution of other defects. This means that the current practice of rating a casting solely by the worst individual defect is unconservative for fatigue-critical applications. A more rational quality evaluation procedure should simultaneously account for the size, position, and spatial distribution of casting defects, as well as the stress state they induce in the structural component.
Concluding Remarks
Based on the extensive numerical simulations performed in this study, the following conclusions can be drawn:
(1) Under static concentrated loading, the size, position, and distribution of casting defects on the cast steel joint have negligible influence on the overall static strength and stiffness of the steel truss. The maximum stress variation among different defect configurations is only about 11.7% for different positions and about 1.7% for different defect sizes. The displacement fields remain almost unchanged. However, casting defects do cause local stress concentration in their immediate vicinity, which may affect crack initiation under cyclic loading.
(2) Under constant-amplitude fatigue loading, the effect of casting defects is strongly amplified. For the same defect grade at different positions, the fatigue life can differ by two orders of magnitude, with some positions leading to an infinite fatigue life while others give a life as low as \(1.91 \times 10^5\) cycles. For a fixed position, increasing the defect grade from Grade 2 to Grade 3 reduces the fatigue life by roughly one order of magnitude. Moreover, the coexistence of multiple defects reduces the fatigue life at a given location by more than 70% compared with the case of a single defect.
(3) The current casting quality rating method specified in GB/T 7233—2009 is insufficient for fatigue-sensitive structures. It relies only on the largest defect size within a predefined evaluation area and completely ignores the defect position and distribution. The present results show that different defect distributions with the same Max defect size can lead to fatigue lives differing by more than an order of magnitude. A reliable quality assessment method should incorporate a stress-based or damage-based criterion that accounts for the actual interaction of casting defects with the local stress field.
(4) Because the size and location of casting defects are inherently random, future work should aim at generating realistic random defect fields through probabilistic modeling. This will enable a more accurate and statistically meaningful evaluation of the influence of casting defects on structural performance. The use of high-fidelity simulation combined with experimental validation will further improve our understanding and lead to more robust design and inspection criteria for cast steel structures.
In summary, this study quantifies the effects of casting defects on both the static and fatigue behavior of steel structures with cast steel joints. The findings highlight the necessity of treating casting defects as a spatial and size-dependent phenomenon rather than a single worst case. By doing so, engineers can better ensure the safety and reliability of cast steel components in demanding applications.