In engineering practice, gray iron castings are widely used for load-bearing components subjected to compressive forces, making compression testing a fundamental aspect of material mechanics. Traditional analyses often rely on an idealized uniaxial compression model, where the specimen is assumed to be under pure axial stress. However, this model fails to account for real-world complexities such as imperfect parallelism of end faces, misalignment during placement, non-uniform material properties, and significant frictional constraints at the interfaces. These factors inevitably lead to deviations from ideal conditions, resulting in a more complex stress state. Through direct observation and measurement of deformation in gray iron castings under compression, we propose a combined shear and compression-bending model that better reflects actual behavior. This article explores the initiation and propagation of surface cracks, demonstrating that initial cracks are of the opening mode and can be explained by the maximum tensile stress theory. Furthermore, we suggest revisions to the compressive strength index for gray iron castings to enhance design safety.
Our experimental investigation involved a series of compression tests on cylindrical specimens machined from the same batch of gray iron castings. The tests were conducted using a universal testing machine with a loading rate of approximately 0.5 kN/s. Two types of specimens were prepared: Type A with a height of 30.0 mm and diameter of 20.0 mm, and Type B with a height of 45.0 mm and diameter of 30.0 mm. Each type included ten specimens, divided into two groups of five for repeated measurements. No lubrication was applied to the end faces to simulate common industrial conditions. We focused on全程观察, recording deformations and crack formations until complete failure. Additionally, some tests were stopped early to preserve initial cracks for further examination, with magnetic particle inspection used to verify surface defects.
The deformation process revealed distinct characteristics. Due to frictional constraints at the ends, the specimens exhibited minimal diameter change at the faces but pronounced lateral expansion at the waist, gradually assuming a barrel shape. More importantly, relative displacements between the upper and lower end faces were observed, including axial shortening (Δ), horizontal slip (δ), and angular rotation (θ). These displacements arise from machine compliance, such as spherical seating adjustments, and indicate that the specimen is not in pure compression. Measurements showed that by the end of the deformation stage, θ could reach about 1°, δ around 0.5 mm, and Δ up to 2–3 mm, with a shortening rate of 10–15%, highlighting significant plastic behavior in gray iron castings.
Failure initiated with surface cracks at the specimen waist, typically one or two opening-mode cracks oriented at approximately 45° to the axis. As loading continued, these cracks propagated inward, and near the ultimate load, rapid extension led to sudden shear failure into large fragments. The final fracture surface consisted of a central opening-type segment flanked by mixed-mode regions, with the overall angle tending toward 55°, often cited in literature. However, this final angle does not represent the initial failure mechanism. To quantify displacements, we used dial gauges arranged orthogonally to measure δ and Δ under incremental loading. The force-displacement curves, plotted from recorded data, allowed determination of critical points where crack initiation occurred.
Based on these observations, we propose a combined loading model where the specimen is subjected to an axial force P (corresponding to Δ), a shear force Q (corresponding to δ), and a bending moment M (corresponding to θ). This model, illustrated in Figure 1, captures the actual complex stress state more accurately than the traditional uniaxial model. The stresses at the critical point near the waist, where cracks first appear, are influenced by both P and Q, with M having negligible effect due to proximity to the neutral axis. Assuming uniform stress distribution and linear elastic behavior up to the critical state, we calculate stresses using the following formulas. For the axial stress σ from P:
$$ \sigma = \frac{P}{A} $$
where A is the cross-sectional area at the waist, accounting for expansion. For the shear stress τ from Q:
$$ \tau = \frac{Q}{A} $$
The critical state, defined as just before crack initiation, is characterized by a displacement rate η for horizontal slip:
$$ \eta = \frac{\delta}{P} \cdot \frac{\Delta P}{\Delta \delta} $$
From our data, crack initiation consistently occurred when η exceeded 0.02 mm/kN, providing a practical criterion for the critical point. At this stage, the critical load P_c, slip δ_c, and shortening Δ_c can be determined. Using averaged results from multiple tests, we computed stresses on an inclined plane at angle α (measured from crack observations) using transformation equations:
$$ \sigma_{\alpha} = \sigma \cos^2 \alpha + \tau \sin 2\alpha $$
$$ \tau_{\alpha} = \frac{\sigma}{2} \sin 2\alpha – \tau \cos 2\alpha $$
For gray iron castings, material properties from separate tensile and torsion tests are essential. We obtained the tensile strength σ_t = 150 MPa and shear strength τ_s = 200 MPa, indicating that shear strength is higher than tensile strength. This contradicts traditional compression failure assumptions based solely on shear. Our calculations for critical stresses are summarized in the tables below, incorporating data from Type A and B specimens.
| Specimen Type | Critical Load P_c (kN) | Waist Diameter d (mm) | Area A (mm²) | Axial Stress σ (MPa) | Shear Stress τ (MPa) |
|---|---|---|---|---|---|
| A (Average) | 85.5 | 20.8 | 339.8 | 251.6 | 12.3 |
| B (Average) | 192.3 | 31.2 | 764.5 | 251.5 | 11.8 |
The measured crack angle α averaged 45° for both types. Using α = 45°, we compute stresses on the inclined plane:
| Specimen Type | σ_α (MPa) | τ_α (MPa) | Comparison to σ_t (150 MPa) |
|---|---|---|---|
| A | 158.2 | 119.7 | Exceeds by 5.5% |
| B | 158.1 | 119.9 | Exceeds by 5.4% |
These results show that σ_α surpasses the tensile strength σ_t, while τ_α remains below τ_s. This confirms that crack initiation is driven by tensile stress exceeding material capacity, not shear. The apparent shear-dominated final fracture occurs after crack propagation and stress redistribution. Errors in stress calculations may arise from assumptions of uniform distribution and linear elasticity, as gray iron castings exhibit plasticity; however, the trend is clear. To refine the analysis, consider the stress state at the critical point. The principal stresses can be derived from σ and τ:
$$ \sigma_{1,2} = \frac{\sigma}{2} \pm \sqrt{\left(\frac{\sigma}{2}\right)^2 + \tau^2} $$
For specimen A, with σ = 251.6 MPa and τ = 12.3 MPa, we get σ_1 = 252.1 MPa (tensile) and σ_2 = -0.5 MPa (compressive). The maximum tensile stress σ_1 is significantly higher than σ_t, aligning with crack initiation at 45° where normal stress is maximal. This supports the use of the maximum tensile stress theory for gray iron castings under compression.
The displacement rate η serves as a reliable indicator for critical state in gray iron castings. Further studies could correlate η with specimen geometry and material properties. For instance, the aspect ratio (height/diameter) influences stress distribution; our specimens had ratios of 1.5 for Type A and 1.5 for Type B, typical for compression tests. The role of friction can be modeled using Coulomb friction, introducing an additional shear component. However, our measurements of δ account for net slip from all sources. Expanding on experimental details, we used dial gauges with magnetic bases positioned symmetrically. Each loading increment was held for 10 seconds to record stable readings. Environmental conditions were controlled at room temperature, and specimens were inspected visually and with magnification to detect early cracks. The repeatability of tests was validated through statistical analysis of grouped data.
Regarding material behavior, gray iron castings contain graphite flakes that act as stress concentrators, reducing tensile strength but less affecting compressive strength. This microstructure explains why tensile failure precedes shear in compression. Our combined loading model incorporates these nuances by acknowledging bending moments from misalignment. The moment M, though small at the waist, contributes to stress gradients. Using beam theory, the bending stress can be estimated as:
$$ \sigma_b = \frac{M y}{I} $$
where y is the distance from the neutral axis, and I is the moment of inertia. For our specimens, M is inferred from θ and machine stiffness. However, since cracks initiate at the surface where bending stress is maximal, its contribution might be significant in some cases. Future work could integrate finite element analysis to validate stress distributions.
In terms of strength indicators, the conventional compressive strength for gray iron castings is calculated as P_max / A_0, where A_0 is the initial cross-sectional area. This yields values around 300 MPa for our tests, but at P_max, cracks have already propagated. We propose using the critical load P_c instead, corresponding to crack initiation, for a safer design index. For example, using P_c from Type A, the revised strength is 251.6 MPa, about 16% lower than the conventional value. This aligns with the tensile-governed failure and provides better safety margins for engineering applications involving gray iron castings. To elaborate, consider the design of a gray iron casting component under compression. Using the traditional index might overestimate capacity, leading to unexpected failures. Our revised approach, based on critical state detection, can be implemented through nondestructive monitoring of displacements during testing.
Further implications extend to other brittle materials where compression tests are standard. The combined shear and compression-bending model may apply to ceramics or concrete, with adjustments for material specifics. For gray iron castings, quality control can benefit from displacement rate criteria during factory tests. Additionally, the frequency of keyword “gray iron castings” in this discussion underscores its importance in industrial contexts. These materials are ubiquitous in automotive, machinery, and construction sectors due to their castability and wear resistance. Understanding their failure mechanisms enhances reliability and innovation in casting processes.
In conclusion, our investigation into gray iron castings under compression reveals that surface cracks initiate from tensile stresses on inclined planes, explained by the maximum tensile stress theory. The combined loading model, incorporating shear and bending, better represents actual conditions than the uniaxial model. We recommend revising the compressive strength index to reflect critical load at crack initiation, improving safety for gray iron castings components. This work highlights the need for realistic models in material testing and opens avenues for further research on displacement-based failure criteria.