## 1 Introduction
These studies have quantitatively analyzed the interaction effects of multiple cracks on fracture mechanics parameters using 3D FEA techniques and verified the conservatism of coalescence criteria specified in existing codes. However, 3D FEA techniques are limited to examining interaction effects only in stationary multiple crack conditions, thus presenting a limitation in assessing the conservatism of coalescence crack shape criteria proposed in existing codes. For this reason, extensive studies have been conducted using 3D iterative FEA to evaluate the conservatism of the coalescence shape criteria in codes that assume multiple cracks coalesce into a single semi-elliptical crack [16; 17; 18; 19]. Iterative FEA is preferred as it simulates crack growth more naturally by calculating crack growth at each node along the crack front [20]. [PERSON] et al. [16] performed 3D iterative FEA using the commercial FEA software Abaqus (2021 version) to simulate fatigue crack growth (FCG) for various single and multiple cracks in piping, verifying the suitability of iterative FEA for crack-growth simulations and identifying an increase in the SIF during coalescence in multiple crack conditions. [PERSON] et al. [17] developed the CRACK-FEM program to simulate FCG for multiple cracks in a plate, validating the effectiveness of CRACK-FEM through comparisons with experimental results. This study fixed the coalescence distance criterion for multiple cracks at a specific distance. [PERSON] et al. [18] utilized S-version FEM to simulate FCG for multiple cracks of varying sizes in a plate to examine the rationality of the coalescence criterion proposed by the JSME Code [21]. Through comparisons between experimental results, FEA results, and the JSME Code methodology, they confirmed that the JSME Code reasonably predicts coalescence behavior. [PERSON] et al. [19] proposed a new coalescence criterion for FCG and SCC crack growth, applied it to ZENCRACK for iterative FEA, and simulated FCG for multiple cracks in a plate. The results were compared with those obtained using methodologies from ASME Section XI, BS 7910, API 579, and GB/T19624 [22], confirming the suitability of the proposed coalescence criteria for multiple cracks. These studies have demonstrated that 3D iterative FEA is suitable for predicting the growth behavior of multiple cracks. However, most studies have focused on applyingexisting coalescence criteria to 3D iterative FEA to evaluate the suitability of current codes. Although some prior studies have proposed new coalescence criteria for multiple cracks, they have not extended to validation through comparisons with experimental results. Therefore, comprehensive studies that propose and validate a new coalescence criterion for multiple cracks thereby examining the conservatism of the coalescence criteria presented in existing codes, remain limited. This study proposes a coalescence criterion based on plastic zone size to simulate the natural growth and coalescence of multiple cracks. This criterion was implemented in the Advanced Iterative Finite Element Method (AI-FEM) algorithm, an automatic crack growth program utilizing re-meshing developed by [PERSON] et al. [23]. Fatigue Crack Growth (FCG) simulations were conducted using AI-FEM for multiple cracks on the same plane within both plate and pipe geometries. The proposed coalescence criterion was validated through comparisons between AI-FEM results and experimental data. Additionally, the new criterion was compared with the ASME Section XI coalescence criterion, allowing for a quantitative analysis of the conservatism in existing codes. This paper is structured as follows: Section 2 reviews coalescence criteria for multiple cracks as presented in various codes. Section 3 details the AI-FEM algorithm, focusing on the proposed plastic zone size-based criteria. Section 4 compares AI-FEM results with experimental data and examines the conservatism of ASME Section XI criteria for plate geometries. Section 5 extends this analysis to pipe geometries.